The locus of a point from which the lengths of the tangents to the circles x^2+y^2=4 and 2(x^2+y^2)-10x+3y-2=0 are equal is

JEE Advanced Mathematics question

The locus of a point from which the lengths of the tangents to the circles and are equal is

(A)a straight line inclined at with the line joining the centres of the circles
(B)a circle
(C)an ellipse
(D)a straight line perpendicular to the line joining the centres of the circlesCorrect

Answer: (D)

Write both circles in standard form (coefficient of equal to 1):

≡ +-4=0, ≡ +-5x+32y-1=0.

The squared tangent lengths from are and ; equating them gives the radical axis

-=5x-32y-3=0,\ i.e. 10x-3y-6=0

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Question ID VK-108964