Question

If a chords of the circle $x^2+y^2=8$ makes equal intercepts of length a on the coordinate axis then a can be

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (A), (B)

The correct options are
A $2$
B $3$

Given equation of circle is
$x^2+y^2=8$
Center $(0,0)$ ,radius $=2\sqrt{2}$
Since, the chord of the circle makes equal intercepts of length $a$ on coordinate axis.
So, equation of chord is given as
$x\pm y=\pm a$
Now, since the chord intersects the given circle at two distinct points .So, the length of perpendicular from $(0,0)$ to the chord is less than radius
$\Rightarrow |\frac{\pm a}{\sqrt{2}}|<2\sqrt{2}$
$\Rightarrow a^2<16$
$\Rightarrow a<4$
$\Rightarrow a$ can be $2$ or $3$