Question

If a chord of the circle $x^2+y^2=32$ makes equal intercepts of length $l$ on the coordinate axes, then $\left|l\right|<$

• A. $2$
• B. $5$
• C. $8$
• D. $7$

Answer 1

The correct option is C $8$

Since the chord makes equal intercept of length $l$ on the coordinate axes, so its equation can be written in the form $x\pm y=\pm l$.

Since the chord intersect the given circle at two distinct points, therefore the length of the $\perp$ from the center $(0,0)$ of the given corcle to the chord must be less than the radius

$\Rightarrow \left|\frac{\pm l}{\sqrt{2}}\right|<\sqrt{32}\Rightarrow l^2<64\Rightarrow \left|l\right|<8$