Question

If a chord of a circle $x^2+y^2=32$ makes equal intercepts of length $l$ on the co-ordinate axes, then

• A. $\ell <8$
• B. $\ell <16$
• C. $\ell >8$
• D. $\ell >16$

Answer 1

The correct option is A $\ell <8$

Since the chord makes equal intercepts of length $l$ on coordinate axes, so the equation can be written as :-

$x\pm y=\pm l$

The length of $\perp$ from centre $(0,0)$ to the chord must be less than radius

$|\pm \frac{l}{\sqrt{2}}|$ > $\sqrt{32}$

$\therefore l^2<64$

$l<8$