Question

If $ m_1 $ and $ m_2 $ are the slopes of tangents to the circle $ x^ 2 + y^ 2 = 4 $ from the point $ (3, 2) $ , then $ m_1 - m_2 $ is equal to

• A. $ \frac{5}{12} $
• B. $ \frac{12}{5} $
• C. $ \frac{3}{2} $
• D. $ 0 $

Answer 1

Answer: (B)

Equation of pair of tangents is
$S S_{1}=T^{2} $
$\Rightarrow \,\,\,\left(x^{2}+y^{2}-4\right)(9+4-4)=(3 x+2 y-4)^{2}$
$\Rightarrow \,\,\, 5 y^{2}+16 y-12 x y+24 x-52=0 $
$\therefore \,\,\, m_{1}+m_{2}=\frac{-2 h}{b}=\frac{12}{5} $
and $\ \,\,\, m_{1} m_{2}=0 $
Now, $\,\,\, m_{1}-m_{2}=\sqrt{\left(m_{1}+m_{2}\right)^{2}-4 m_{1} m_{2}} $
$=\sqrt{\left(\frac{12}{5}\right)^{2}-0} $
$=\frac{12}{5}$