Question

If the two circles which pass through $(0,3)$ and $(0,–3)$ and touch the line $y=mx+5$, cut each other orthogonally, then the value of $m^2$ will be

• A. $\frac{7}{6}$
• B. $\frac{7}{5}$
• C. $\frac{7}{3}$
• D. $\frac{7}{9}$

Answer 1

The correct option is D $\frac{7}{9}$

Applying condition of orthogonality we get
$5^2=9(2+m^2)$
$\Rightarrow m^2=\frac{25}{9}-2$
$m^2=\frac{7}{9}$