If (a, 0) is a point on a diameter segment of the circle x …

Maths Circle and System of Circles General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If (a, 0) is a point on a diameter segment of the circle x 2 + y 2 = 4, then x 2 – 4x – a 2 = 0 has

exactly one real root in (– 1, 0]

Exactly one real root in [2, 5]

distinct roots greater than-1

Distinct roots less than 5

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a,b,c,d)Since (a, 0) is a point on the diameter of the circle x 2 + y 2 = 4,

So maximum value of a 2 is 4

Let f(x) = x 2 – 4x – a 2

clearly f (–1) = 5 – a 2 is 4

f(2) = – (a 2 + 4) < 0

f(0) = – a 2 < 0 and f(5) = 5 – a 2 > 0

so graph of f(x) will be as shown

Hence , ( , , are the correct answer

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