Question

If a straight line through $C(-\sqrt{8},\sqrt{8})$ making an angle of ${135}^o$ with the X-axis cuts the circle $x=5\cos \theta ,y=5\sin \theta$ at points A and B, then the length of AB is?

Answer 1

Slope of the line = $-1$

Equation of the line : $(y-\sqrt{8})=-(x+\sqrt{8})$

$y+x=0$

Equation of the circle - $x^2+y^2=5$

$2y^2=5$

$y^2=\frac{5}{2}$

$y=\pm \sqrt{\frac{5}{2}}$

$x=\mp \sqrt{\frac{5}{2}}$

Hence, Distance between $AB=\sqrt{(2\sqrt{\frac{5}{2}}{)}^2+(2\sqrt{\frac{5}{2}}{)}^2}$

$AB=\sqrt{20}$