Amit M Agarwal Solutions for Chapter: Ellipse, Exercise 3: Work Book Exercise 15.3

Chords of an ellipse are drawn through the positive end of the minor axis. Then, their midpoint lies on

The area of rectangle formed by the perpendiculars from the centre of an ellipse to the tangent and normal at the point, whose eccentric angle is $\pi /4$ is

If the chords of contact of tangent from two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ are at right angles, then $\frac{x_1{x}_2}{y_1{y}_2}$is equal to

The locus of the point of intersection of perpendicular tangents to $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{a^2+\lambda }+\frac{y^2}{b^2+\lambda }=1$ is

The locus of the midpoints of the chords $2x+3y+\lambda =0$ of the ellipse $x^2+4y^2=1$, $\lambda$ being a parameter, is

In the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ the length of perpendiculars from the centre upon all chords which join ends of perpendicular diameters, is