A variable circle passes through the point A (a,

Maths Circle and System of Circles General Numeric Response

Published on: August 12, 2026

& touches the x − axis and the locus of the other end of the diameter through A is (x − a)² = λ by , then find the value of λ

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The correct answer is:

(4)Equation of circle whose diameter's end points are (a, and (h, k)

(x – a) (x – h) + (y – (y – k) = 0

x 2 + y 2 – x(a + h) – y(b + k) + ah + bk = 0

it touches x-axis.

Hence g 2 = c ⇒ = ah + bk ⇒ (h – a) 2 = 4bk

∴ Locus of (h, k) is (x – a) 2 = 4by.

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