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<Input><Text-field style="Text" layout="Normal">Para_f_d gives the equation of a parabola defined by its focus (a,b) and its directrix (x=d). </Text-field><Text-field style="Text" layout="Normal">Credit:https://www.khanacademy.org/math/algebra2/intro-to-conics-alg2/focus-and-directrix-of-a-parabola-alg2/v/equation-for-parabola-from-focus-and-directrix</Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="true" style="2D Input" input-equation="para_f_d := proc (a, b, d) options operator, arrow; (1/2)*(x-a)^2/(b-d)+(1/2)*b+(1/2)*d end proc:" display="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">QyQ+SSlwYXJhX2ZfZEc2ImYqNiVJImFHRiVJImJHRiVJImRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwoKiYsJkkieEdGJSIiIjkkISIiIiIjLCY5JUYyOSZGNEY0I0YyRjVGN0Y5RjhGOUYlRiVGJUY0</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">Grab two parabolas defined by different focii and the same directrix. </Text-field><Text-field style="Text" layout="Normal">In order to find where they cross, we set the equations equal to each other</Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="para_f_d(a, b, d) = para_f_d(r, s, d)" display="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">Ly1JKXBhcmFfZl9kRzYiNiVJImFHRiVJImJHRiVJImRHRiUtRiQ2JUkickdGJUkic0dGJUYp</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywoKiYsJkkieEc2IiIiIkkiYUdGJyEiIiIiIywmSSJiR0YnRihJImRHRidGKkYqI0YoRitGLUYvRi5GLywoKiYsJkYmRihJInJHRidGKkYrLCZJInNHRidGKEYuRipGKkYvRjVGL0YuRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We let maple solve the equation since it is rather nasty, however we specify that the directrix is always greater than the y values of the two focii.</Text-field>
</Input>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L3" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="solve([(1/2)*(x-a)^2/(b-d)+(1/2)*b+(1/2)*d = (1/2)*(x-r)^2/(s-d)+(1/2)*s+(1/2)*d, b < d, s < d], x)" display="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">LUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDclLywoKiYsJkkieEdGJyIiIkkiYUdGJyEiIiIiIywmSSJiR0YnRi9JImRHRidGMUYxI0YvRjJGNEY2RjVGNiwoKiYsJkYuRi9JInJHRidGMUYyLCZJInNHRidGL0Y1RjFGMUY2RjxGNkY1RjYyRjRGNTJGPEY1Ri4=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We manually factor the expressions since Maple seems unable to.</Text-field><Text-field style="Text" layout="Normal">Note that the points may not be colinear along the x direction given this solution.</Text-field>
</Input>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L7" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="para_f_d_intersect1 := proc (a, b, r, s, d) options operator, arrow; (a*(d-s)+r*(b-d)+sqrt((d-b)*(d-s)*((a-r)^2+(b-s)^2)))/(b-s) end proc:" display="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">QyQ+STRwYXJhX2ZfZF9pbnRlcnNlY3QxRzYiZio2J0kiYUdGJUkiYkdGJUkickdGJUkic0dGJUkiZEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsKComOSQiIiIsJjkoRjQ5JyEiIkY0RjQqJjkmRjQsJjklRjRGNkY4RjRGNC1JJXNxcnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyooLCZGNkY0RjxGOEY0RjVGNCwmKiQsJkYzRjRGOkY4IiIjRjQqJCwmRjxGNEY3RjhGSEY0RjRGNEY0RkpGOEYlRiVGJUY4</Equation></Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="para_f_d_intersect2 := proc (a, b, r, s, d) options operator, arrow; (a*(d-s)+r*(b-d)-sqrt((d-b)*(d-s)*((a-r)^2+(b-s)^2)))/(b-s) end proc:" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVE0cGFyYV9mX2RfaW50ZXJzZWN0MkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYkLUYjNi0tRiw2JVEiYUYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRImJGJ0YvRjJGVy1GLDYlUSJyRidGL0YyRlctRiw2JVEic0YnRi9GMkZXLUYsNiVRImRGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSgmc3JhcnI7RidGOUY7Rj5GQEZCRkRGRkZIRmVuL0ZORmZuLUkmbWZyYWNHRiQ2KC1GIzYuRlQtRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmpvLUZQNiQtRiM2J0Ziby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORltxRl9vRmVvRjlGOS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmpvLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGanBGXHFGXG9GYHAtRlA2JC1GIzYnRmluRmdwRmJvRmVvRjlGOUZncC1JJm1zcXJ0R0YkNiMtRiM2KC1GUDYkLUYjNiZGYm9GZ3BGaW5GOUY5RmBwLUZQNiQtRiM2JkZib0ZncEZfb0Y5RjlGYHAtRlA2JC1GIzYmLUklbXN1cEdGJDYlLUZQNiQtRiM2JkZURmdwRlxvRjlGOS1GIzYlLUkjbW5HRiQ2JFEiMkYnRjlGL0YyLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZgcS1GaXI2JS1GUDYkLUYjNiZGaW5GZ3BGX29GOUY5Rl9zRmVzRjlGOUY5RmVvRjktRiM2J0ZpbkZncEZfb0YvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmV0LyUpYmV2ZWxsZWRHRj0tRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GZW9GOQ==">QyQ+STRwYXJhX2ZfZF9pbnRlcnNlY3QyRzYiZio2J0kiYUdGJUkiYkdGJUkickdGJUkic0dGJUkiZEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsKComOSQiIiIsJjkoRjQ5JyEiIkY0RjQqJjkmRjQsJjklRjRGNkY4RjRGNC1JJXNxcnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyooLCZGNkY0RjxGOEY0RjVGNCwmKiQsJkYzRjRGOkY4IiIjRjQqJCwmRjxGNEY3RjhGSEY0RjRGOEY0RkpGOEYlRiVGJUY4</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">Test the solutions.</Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="para_f_d(1, 2, 14)" display="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">LUkpcGFyYV9mX2RHNiI2JSIiIiIiIyIjOQ==</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2KC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGLy1GTDYkUSMyNEYnRi8vJS5saW5ldGhpY2tuZXNzR0ZOLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlYvJSliZXZlbGxlZEdGNC1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFRmluLUYjNiQtSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiQtRiM2Ji1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkRGS0YvRi8tRkw2JFEiMkYnRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRi8vJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjRGLy1GLDYtUSIrRidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GTDYkUSI4RidGL0Yv">LCYqJCwmSSJ4RzYiIiIiISIiRiciIiMjRigiI0MiIilGJw==</Equation></Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="para_f_d(5, 4, 14)" display="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">LUkpcGFyYV9mX2RHNiI2JSIiJiIiJSIjOQ==</Equation></Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="plot([-(1/24)*(x-1)^2+8, -(1/20)*(x-5)^2+9], x = -2 .. 2)" display="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">LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkNyQsJiokLCZJInhHRiciIiIhIiJGLiIiIyNGLyIjQyIiKUYuLCYqJCwmRi1GLiEiJkYuRjAjRi8iIz8iIipGLi9GLTshIiNGMA==</Equation></Text-field>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="evalf(para_f_d_intersect2(1, 2, 5, 4, 14))" display="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">LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMtSTRwYXJhX2ZfZF9pbnRlcnNlY3QyRzYiNiciIiIiIiMiIiYiIiUiIzk=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEsNDkuNDk0ODk3NDNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JCIrVigqW1xcISIp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we tackle the simpler case of focii colinear on the x axis. The solution is simply the average of the x values.</Text-field>
</Input>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L42" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="para_f_d(a, b, d) = para_f_d(r, b, d)" display="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">Ly1JKXBhcmFfZl9kRzYiNiVJImFHRiVJImJHRiVJImRHRiUtRiQ2JUkickdGJUYoRik=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUYjNigtRiM2KC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYzNiRRIjJGJ0Y2LyUubGluZXRoaWNrbmVzc0dGNS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZALyUpYmV2ZWxsZWRHUSZmYWxzZUYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjYvJSZmZW5jZUdGRS8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZaLUYwNigtRiM2Ji1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y3USdpdGFsaWNGJy1GRzYtUSgmbWludXM7RidGNkZKRkxGTkZQRlJGVEZWL0ZZUSwwLjIyMjIyMjJlbUYnL0ZmbkZgcC1GZG82JVEiYUYnRmdvRmpvRjZGNkY5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGRUY2LUYjNiYtRiM2Ji1GZG82JVEiYkYnRmdvRmpvRlxwLUZkbzYlUSJkRidGZ29Gam9GNkZocEZbcUY2RjxGPkZBRkNGaHBGW3FGNi1GRzYtUSIrRidGNkZKRkxGTkZQRlJGVEZWRl9wRmFwLUYjNihGL0ZGLUYjNiRGYXFGNkZocEZbcUY2RmdxLUYjNihGL0ZGLUYjNiRGZHFGNkZocEZbcUY2RjYtRkc2LVEiPUYnRjZGSkZMRk5GUEZSRlRGVi9GWVEsMC4yNzc3Nzc4ZW1GJy9GZm5GZnItRiM2KC1GIzYoRi9GRi1GMDYoLUYjNiYtRlxvNiUtRl9vNiQtRiM2JkZjb0ZccC1GZG82JVEickYnRmdvRmpvRjZGNkY5RmVwRmhwRltxRjZGXXFGPEY+RkFGQ0ZocEZbcUY2RmdxRmpxRmdxRl5yRjZGaHBGW3FGNg==">LywoKiYsJkkieEc2IiIiIkkiYUdGJyEiIiIiIywmSSJiR0YnRihJImRHRidGKkYqI0YoRitGLUYvRi5GLywoKiYsJkYmRihJInJHRidGKkYrRixGKkYvRi1GL0YuRi8=</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L56" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="solve((1/2)*(x-a)^2/(b-d)+(1/2)*b+(1/2)*d = (1/2)*(x-r)^2/(b-d)+(1/2)*b+(1/2)*d, x)" display="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">LUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC8sKComLCZJInhHRiciIiJJImFHRichIiIiIiMsJkkiYkdGJ0YuSSJkR0YnRjBGMCNGLkYxRjNGNUY0RjUsKComLCZGLUYuSSJyR0YnRjBGMUYyRjBGNUYzRjVGNEY1Ri0=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L57" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
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</Worksheet>