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Maths Circle and System of Circles Chord of Contact of Tangent, Pole and Polar Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The values of α for which the point ( α – 1, α + 1) lies in the larger segment of the circle

x 2 + y 2 – x – y – 6 = 0 made by the chord whose equation is x + y – 2 = 0 is -

– 1 < α < 1

1 < α < ∞

– ∞ < α < – 1

α ≤ 0

Text Solution

Verified by Experts

The correct answer is:

Circle S = x 2 + y 2 – x – y – 6 = 0

centre at (1/2, 1/2)

P( α – 1, α + 1) must lie inside the circle

So ( α – 1) 2 + ( α + 1) 2 – ( α – 1) – ( α + 1) – 6 < 0

α 2 – α – 2 < 0 ⇒ ( α – 2) ( α + 1) < 0

– 1 < α < 2 … (1)

Also P and C must lie on the same side of the line L = x + y – 2 = 0

L(1/2, 1/2) and L( α – 1, α + 1) must have same sign L = + = – 1 < 0

L( α – 1, α + 1) = α – 1 + α + 1 – 2 < 0

α < 1 …(2)

By both the inequalities – 1 < α < 1.

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