Question

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

• A. 5
• B. 10
• C. 15
• D. $15\sqrt{2}$

Answer 1

The correct option is B 10

Inclination of the line $\overleftrightarrow{AB}$ is ${135}^{\circ }\Rightarrow Slope=tan{135}^{\circ }=-1$
Equation of $\overleftrightarrow{AB}$ is $y-\sqrt{8}=-1(x+\sqrt{8})\Rightarrow x+y=0$
x + y = 0 passes through the centre of the circle $x^2+y^2=25$
$\therefore$ Length of the chord AB = Diameter of the circle =$2\times 5=10$