﻿ Let a circle be given by 2x(x – a) + y(2y – b) = 0, (a ≠ 0, b ≠ 0). Find the condition on a and b, if two chords each bisected by the x – axis can be drawn to the circle from  : Kaysons Education

# Let A Circle Be Given By 2x(x – a) + y(2y – b) = 0, (a ≠ 0, b ≠ 0). Find The Condition On A And B, If Two Chords Each Bisected By The x – Axis Can Be Drawn To The Circle From

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## Question

### Solution

Correct option is

a2 > 2b2.

Equation of the given circle is

2x (x – a) + y (2y – b) = 0

or      2x2 – 2ax + 2y2 – by = 0

or        x2 + y2 – ax – b/2 y = 0                       …(1)

Since the two chords are bisected by x-axis so let (h, 0) be the mid point where h has two real values.

Equation of the chord is

T = S1

It passes through (ab/2)

Since the value of h are real and distinct so

B2 – 4AC > 0

a2 – 2b2 > 0

a2 > 2b2.

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