Question

The angle subtended by common tangents of two ellipses $4(x-4{)}^2+25y^2=100$ and $4(x+1{)}^2+y^2=4$ at the origin is

• A. $\pi /3$
• B. $\pi /4$
• C. $\pi /6$
• D. $\pi /2$

Answer 1

Answer: (D)

$\frac{(x-4{)}^2}{25}+\frac{y^2}{4}=1$
and $(x-1{)}^2+\frac{y^2}{4}=1$
Clearly, $m_{OP}\cdot m_{OQ}=-1$
Therefore, $OP$ and $OQ$ are perpendicular to each other,