Embibe Experts Solutions for Exercise 15: Assignment

Number of points on the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ from which pair of perpendicular tangents are drawn to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, is

The equation of the chord of the ellipse $x^2+4y^2=4$ having the middle point at $\left(-1, \frac{1}{2}\right)$ is

Pole of the line $x+4 y=5$ with respect to the ellipse $5x^2+4y^2=10$ is

The locus of the mid points of the portion of the tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ intercepted between the axes is

A rod of given length moves such that its extremities lie on two fixed perpendicular lines. Any point (other than mid point) on the rod describes

The locus of the feet of the perpendiculars drawn from the centre to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ on any tangent to it is

The locus of the foot of the perpendicular from any focus upon any tangent to $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is

The locus of the foot of perpendicular from the centre on any tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is