Question

If the circles $x^2+y^2-8x-6y+21=0$ and $x^2+y^2+ay-15=0$ are orthogonal then the value of $a$ is

• A. $-1$
• B. $-2$
• C. $-4$
• D. $-\frac{1}{2}$

Answer 1

The correct option is B $-2$

General equation of circle is given by $x^2+y^2+2gx+2fy+c=0$
Condition for orthogonality of two circles is given by
$2g_1{g}_2+2f_1{f}_2=c_1+c_2$
$\therefore 2\times (-4)\times 0+2\times (-3)\times \left(\frac{a}{2}\right)=21-15\Rightarrow -3a=6\Rightarrow a=-2$