Question

The pair of straight lines joining the origin to the points of intersection of the line y = $2\sqrt{2}x+c$ and the circle $x^2+y^2=2$ are at right angles, if

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Homogenising the curve, we get

$x^2+y^2-2{\left(\frac{y-2\sqrt{2}x}{c}\right)}^2=0$ ---------(1)

But lines represented by (i) are perpendicular.Hence coofficient of $x^2$ + coefficient of $y^2$ = 0

$\Rightarrow 1-\frac{16}{c^2}+1-\frac{2}{c^2}=0\Rightarrow \frac{18}{c^2}=2\Rightarrow c^2-9=0$.