Question

A circle C₁ is drawn having any point P on x- axis as its centre and passing through the centre of the circle

(3) = x² + y² = 1. A common tangent to C₁ and C intersects the circles at Q and R respectively. Then Q(x,y) always satisfies

• A. x² – 1 = 0
• B. x² + y² = 1
• C. y² –1 = 0
• D. None

Answer 1

Answer: (A)

x² – 1 = 0

Answer 2

Let the circle C₁ be (x – a)² + y² = 1

Let Q (x₁, y₁) be the point on it.

tangent at Q is xx₁ + yy₁ – a(x + x₁) = 0

this is also a tangent to x² + y² = 1

Ž $\frac { \left| \alpha x _ { 1 } \right| } { \sqrt { \left( x _ { 1 } - \alpha \right) ^ { 2 } + y _ { 1 } ^ { 2 } } }$ = 1

Ž |x₁| = 1.