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Question

True or False

Statement: Polar of the point P(x1, y1) with respect to the circle x2 + y2 = a2 is xx1 + yy1 = a2 (P is inside the circle)


A

True

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B

False

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Solution

The correct option is A

True


The given situation can be represented as below. Let a random straight line passing through P intersects the circle at R and S. The tangents at R and S intersects at T. Polar is the locus of all such Ts.

Let T (h, k)

Then RS is chord of contact of T which is given by equation,

hx + ky = a2 This passes through (x1, y1)

x1h + y1h = a2

Hence the locus of T is,

xx1 + yy1 = a2, which implies the given statement to be true.


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