Question

The line $2x+y=3$ intersects the ellipse $4x^2+y^2=5$ at two points. The tangents to the ellipse at these two points intersect at the point

• A. $(\frac{5}{3},\frac{5}{3})$
• B. $(\frac{5}{3},\frac{5}{6})$
• C. $(\frac{5}{6},\frac{5}{6})$
• D. $(\frac{5}{6},\frac{5}{3})$

Answer 1

The correct option is D

$(\frac{5}{6},\frac{5}{3})$

Suppose the tangent intersect at $(h,k),$ then equation of chord of contact is

$4hx+ky=5$

But the equation of chord of contact is $2x+y=3$

$\Rightarrow \frac{4h}{2}=\frac{k}{1}=\frac{5}{3}$

$\Rightarrow h=\frac{5}{6},k=\frac{5}{3}$

Thus, required point is $(\frac{5}{6},\frac{5}{3})$