Dr. SK Goyal Solutions for Chapter: Ellipse, Exercise 1: INTRODUCTORY EXERCISE 6.1

The eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ whose latus rectum is half of its major axis, is:

If $\tan \alpha \tan \beta =-\frac{a^2}{b^2}$, then the chord joining two points $\alpha$ and $\beta$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ will subtend a right angle at:

Let $P$ be a variable point on the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ with foci at $S$ and $S\text{'}$. If $A$ be the area of triangle $PSS\text{'}$, then the maximum value of $A$ is:

The length of the major axis of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is three times the length of minor axis, it eccentricity is :

Find the latus rectum, eccentricity, coordinates of the foci, coordinates of the vertices, the length of the axes and the centre of the ellipse $4x^2+9y^2-8x-36y+4=0$.

The distance between the foci of an ellipse is $10$ and its latus rectum is $15 ;$ find its equation referred to its axes as axes of coordinates.

Find the equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point $\left(2,-3\right)$ one focus at $\left(3,-3\right)$ and one vertex at $\left(4,-3\right)$.

Let $P$ be a variable point on the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ with foci at $S$ and $S^{\text{'}}.$ If $A$ be the area of triangle $PS{S}^{\text{'}}$, then the maximum value of $A$ is :