Question

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

• A. $5$
• B. $10$
• C. $25$
• D. $16$

Answer 1

The correct option is A $5$

Clearly, $A=(5\cos \theta ,0)$

and $B=(0,5\sin \theta )$

$AB=\sqrt{{(5\cos \theta -0)}^2+{(5\sin \theta -0)}^2}$

$AB=\sqrt{25({\cos }^2\theta +{\sin }^2\theta )}=\sqrt{25}=5$