Question

Tangents are drawn from any point on the circle $x^2+y^2+2gx+2fy+c=0$ to the circle $x^2+y^2+2gx+2fy+csi{n}^2\alpha +(g^2+f^2)co{s}^2\alpha =0$,then the angle between the tangents

• A. $\alpha$
• B. $2\alpha$
• C. $\frac{\alpha }{2}$
• D. $\frac{3\alpha }{2}$

Answer 1

Answer: (B)

$2\alpha$

$S_1:x^2+y^2+2gx+2fy+c=0$ and $S_2:x^2+y^2+2gx+2fy+csi{n}^2\alpha +(g^2+f^2)co{s}^2\alpha =0$

So, $\sin \theta =\frac{r_2}{r_1}=\frac{\sqrt{(g^2+f^2-c)si{n}^2\alpha }}{\sqrt{g^2+f^2-c}}$

$\sin \theta =sin\alpha$

So, $\theta =\alpha .$

So, angle bet tangents is $2\theta =2\alpha$