Find the length of intercept made by the circle $x^{2} + y^{2} + 2 x + 3$ -5=0 on:

x axis

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y axis

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on the line x = y chord cut by the circle intercept

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None of these

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Solution

The correct option is C x axis
We have,

Equation of circle is

$x^{2} + y^{2} + 2 x + 3 - 5 = 0$

$\Rightarrow x^{2} + y^{2} + 2 x - 2 = 0$

On comparing that we get

$x^{2} + y^{2} + 2 g x + 2 f y + c = 0$

$g = 1$

$f = 0$

$c = - 2$

Centre $(- g, - f) = (- 1, 0)$

Then,

$x = - 1, y = 0$

$(- 1, 0) (o n X - a x i s)$
Hence, this is the answer.

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