Question

The equation of director circle to the circle $x^2+y^2=8$ is

• A. $x^2+y^2=8$
• B. $x^2+y^2=16$
• C. $x^2+y^2=4$
• D. $x^2+y^2=12$

Answer 1

The correct option is B $x^2+y^2=16$

Given

equation of circle is $x^2+y^2=8$ ----- $\left(1\right)$

For director circle centers are same but radius of director circle $=\sqrt{2}$ radius of original circle.

the

$r^1=\sqrt{2}r$

$r^1=\sqrt{2}\times 2\sqrt{2}=4$

now

equator of director circle is

$x^2+y^2=(4{)}^2$

or $x^2+y^2=16$ ------ $\left(2\right)$