Question

A chord of the circle $x^2+y^2=8$ makes equal intercepts on the coordinate axes. If the length of each intercept is '$a$' then the range of '$a$' is

• A. $(-2,2)$
• B. $(-4,4)$
• C. $(-2\sqrt{2},2\sqrt{2})$
• D. $(-1,1)$

Answer 1

The correct option is B $(-4,4)$

$e{q}^n$ of line which makes equal intercept of coordinate ones is $x+y=a$
for limiting condition $x+y=a$ chord could be diameter of circle, than
$a=0$
and limiting condition $x+y=a$ cord could be tangent to circle
$so,2\sqrt{2}=\left|\frac{a}{\sqrt{2}}\right|$
$a=4,-4$
so, range of a $ϵ(-4,4)$