The equation of pair of straight lines joining the point of intersection of the curve $x^{2} + y^{2} = 4$ and y - x = 2 to the origin, is

$x^{2} + y^{2} = (y - x)^{2}$

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$x^{2} + y^{2} + (y - x)^{2} = 0$

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$x^{2} + y^{2} = 4 (y - x)^{2}$

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$x^{2} + y^{2} + 4 (y - x)^{2} = 0$

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Solution

The correct option is A
$x^{2} + y^{2} = (y - x)^{2}$

Equation can be formed by homogenising the curve w.r.t. line.

i.e., $x^{2} + y^{2} = 4 {(\frac{y - x}{2})}^{2}$ or $x^{2} + y^{2} = (y - x)^{2}$ .

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Similar questions

The equation of pair of straight lines joining the point of intersection of the curve $x^{2} + y^{2} = 4$ and y - x = 2 to the origin, is

\sqrt{3} x + y = 2

y^{2} - x^{2} = 4

The equation of the line joining origin to the points of intersection of the curve $x^{2} + y^{2} = a^{2}$ and $x^{2} + y^{2} - a x - a y = 0$ is

x^{2} + y^{2} = a^{2} .

2 c^{2} = a^{2} (1 + m^{2}) .

\sqrt{3} x + y = 2

y^{2} - x^{2} = 4

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