Question

Angle subtended by common tangents intercepted between two ellipses $4(x-4{)}^2+25y^2=100$ and $4(x+1{)}^2+y^2=4$ at origin is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

$\frac{(x-4{)}^2}{25}+\frac{y^2}{4}=1$
and
$(x+1{)}^2+\frac{y^2}{4}=1$
From the diagram ,it is clear that equations of common tangents are $y=\pm 2$
Also $m_{OP}.m_{OQ}=-1$
$\Rightarrow OP$ and $OQ$ are perpendicular to each other.