Question

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

• A. $\left|l\right|<8$
• B. $\left|l\right|<16$
• C. $\left|l\right|>8$
• D. none of these

Answer 1

Answer: (A)

$\left|l\right|<8$

Since the chord makes equal intercepts 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 circle to the chord must be less than the radius

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