Question

The locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ forms a triangle of constant area with the coordinate axes, is

• A. A straight line
• B. A hyperbola
• C. An ellipse
• D. A circle

Answer 1

The correct option is B A hyperbola

The chord of contact of tangents from $\left(x_1{y}_1\right)is\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}=1$
It meets the axes at the points $(\frac{a^2}{x},0)$ and $(0,\frac{b^2}{y_1})$
Area of the triangle is $\frac{1}{2}.\frac{a^2}{x_1}.\frac{b^2}{y_1}$ [constant]
$\Rightarrow$ $x_1{y}_1=\frac{a^2{b}^2}{2k}=c^2$ where c is a constant.
$\Rightarrow$ $xy=c^2$ is the required locus.