Question

If a chord of the circle $x^2+y^2=8$ makes equal intercepts of length $a$ on the coordinate axes, then

• A. $\left|a\right|<8$
• B. $\left|a\right|<4\sqrt{2}$
• C. $\left|a\right|<4$
• D. $\left|a\right|>4$

Answer 1

Answer: (C)

$\left|a\right|<4$

Since the chord makes equal intercepts of length $a$ on the coordinate aces.

So, its equation can be written as $x\pm y=\pm a$

This line meets the given circle at two distinct points.

So, length of the perpendicular from the center $(0,0)$ of the given circle must be less than the radius

i.e $|\pm \frac{a}{\sqrt{2}}|<8\Rightarrow a^2<16\Rightarrow \left|a\right|<4$