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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.

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It is given that the sum of the distances from the point (3,0) and (9,0) is 12.

Let the point be (x, y)

Distance between the point of intersection & centre

Squaring both the sides,

x2 + 12x + 36 = 4x2 - 24x + 36 + 4y + 2

3x2 - 36x + 4y2=0

Hence, the required equation is 3x2 - 36x + 4y2 = 0.

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