Question

Let $P(x_1,y_1)$ and $Q(x_2,y_2)$ where $y_1>0,y_2>0$, be the end points of the latus rectum of the ellipse $x^2+4y^2=4$. Then

• A. $PQ=1$
• B. $PQ=2\sqrt{3}$
• C. $\Delta OPQ$ is acute angled triangle
• D. $\Delta OPQ$ is obtuse angled triangle

Answer 1

Answer: (B), (D)

The correct options are
B $PQ=2\sqrt{3}$
D $\Delta OPQ$ is obtuse angled triangle

Equation of ellipse : $\frac{x^2}{4}+y^2=1\Rightarrow a=2,b=1$
and $e=\frac{\sqrt{3}}{2}$
$\therefore P=(\sqrt{3},\frac{1}{2}),Q=(-\sqrt{3},\frac{1}{2})$
$\Rightarrow PQ=2\sqrt{3}$
Slope of OP $=\frac{1}{2\sqrt{3}}\Rightarrow \angle POQ$ is obtuse