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  • Find the equation of the set of all points the sum of whose distances from the points (3, 0) and (9, 0) is 12.

Find the equation of the set of all points the sum of whose distances from the points (3, 0) and (9, 0) is 12.

Answers (1)

Let the coordinates of the variable point be (x,y)

 Then according to the question \sqrt{\left ( x-3 \right )^{2}+y^{2}}=12-\sqrt{\left ( x-9 \right )^{2}+y^{2}}

x2-6x+9+y2=144+x^{2}-18x+81+y^{2}-24\sqrt{\left (x-9 \right )^{2}+y^{2}}

\left ( x-18 \right )=-2\sqrt{\left (x-9 \right )^{2}+y^{2}}

Again squaring both sides, we get 

x2-36x+324=4(x2-18x+81+y2)

3x2+4y2-36x=0  which is an ellipse.

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infoexpert22

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