Let $P (1, 1)$ be a point inside the circle $x^{2} + y^{2} + 2 x + 2 y - 8 = 0.$ The chord $A B$ is drawn passing through the point $P .$ If $\frac{P A}{P B} = \frac{\sqrt{5} - 2}{\sqrt{5} + 2},$ then equation of chord $A B$ is

y = 2 x + 1

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y = x

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y = - x

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y = \sqrt{2} x + 1

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Solution

The correct option is B $y = x$
$x^{2} + y^{2} + 2 x + 2 y - 8 = 0$
Centre is $C (- 1, - 1)$ and radius is $r = \sqrt{1 + 1 + 8} = \sqrt{10}$
$C P = 2 \sqrt{2}$

$\frac{P A}{P B} = \frac{\sqrt{10} - 2 \sqrt{2}}{\sqrt{10} + 2 \sqrt{2}}$
$\Rightarrow A B$ is a diameter.
$∴$ Equation of $A B$ is $y = x$

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Let P(1,1) be a point inside the circle x2+y2+2x+2y−8=0. The chord AB is drawn passing through the point P. If PAPB=√5−2√5+2, then equation of chord AB is

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