Question

A line meets an ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$ at $A$ and $B$, and tangents to the ellipse at $A$ and $B$ are perpendicular to each other. Then the point of intersection of the tangents may be

• A. $(1,2)$
• B. $(2,3)$
• C. $(1,4)$
• D. None of these

Answer 1

Answer: (A)

$(1,2)$

The point of intersection of two perpendicular tangents meet at director circle of an ellipse.
Equation of the director circle is $x^2+y^2=a^2+b^2=4+1=5$
Only option 'A' satisfies the director circle.
Hence, option 'A' is correct.