A circle C 1 is drawn having any point P on x- axis as its …

Maths Circle and System of Circles Mix Single Correct MCQ

Published on: August 14, 2026

A circle C 1 is drawn having any point P on x- axis as its centre and passing through the centre of the circle

x 2 – 1 = 0

x 2 + y 2 = 1

= x 2 + y 2 = 1. A common tangent to C 1 and C intersects the circles at Q and R respectively. Then Q(x,y) always satisfies y 2 –1 = 0

None

Text Solution

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The correct answer is:

Let the circle C 1 be (x – α ) 2 + y 2 = 1

Let be the point on it.

tangent at Q is xx 1 + yy 1 – α (x + x 1 ) = 0

this is also a tangent to x 2 + y 2 = 1

⇒ = 1

⇒ | | = 1.

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