Question

The tangent and normal to the ellipse $x^2+4y^2=4$ at a point P$\left(\theta \right)$ on it meets the major axes in Q and R respectively.If QR=2, then cos $\theta$ is equal to

• A. $\frac{-4}{5}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $-\frac{2}{3}$

Answer 1

Answer: (B), (D)

The correct options are
B $\frac{2}{3}$
D $-\frac{2}{3}$

$\frac{x^2}{4}+\frac{y^2}{1}=1$

At a point $P\left(0\right)$

Tangent $\to \frac{x\cos \theta }{2}+y\sin \theta =1$

Normal $\to 2x\sec \theta -by\csc \theta =4-1=3$

$Q$ is $(2\sec \theta ,0)$

$R$ is $\left(\frac{3}{2}\right)$

$QR=2.=|\frac{2}{\cos \theta }-\frac{3}{2}\cos \theta |$

$\cos \theta =\frac{2}{3},\frac{-2}{3}$

$B,D$ are connect.