Question

Locus of the point of intersection of the tangents at the end points of the focal chord of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\left(b⟨a\right)$ is

• A. $y=\pm \frac{b^2}{\sqrt{a^2-b^2}}$
• B. $x=\pm \frac{ab}{\sqrt{a^2-b^2}}$
• C. $x=\pm \frac{a^2}{\sqrt{a^2-b^2}}$
• D. None of these

Answer 1

The correct option is C $x=\pm \frac{a^2}{\sqrt{a^2-b^2}}$

By the property of ellipse,
That if two tangents
interests at focal cord
they meet at that point
on the ellipse
so,
$\begin{array}{c}x=\pm \frac{a}{e}\\ =\pm \frac{a}{\sqrt{1-\frac{b^2}{a^2}}}\\ x=\pm \frac{a^2}{\sqrt{a^2-b^2}}\end{array}$