Question

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

Find the length of segment AB.

Answer 1

Eliminating $\theta$ the circle is x${}^2$ + y${}^2$ = 25
The line through $(-\sqrt{8},\sqrt{8})$
and having slope tan 135${}^{\circ }$ = -1 is
y - $\sqrt{8}$ = -1 (x + $\sqrt{8}$) or y = - x
The line y + x = 0 passes through the centre (0, 0) of the circle x${}^2$ + y${}^2$ = 25.

Hence it is a diameter, say AB, whose length is 2r = 10.