Embibe Experts Solutions for Chapter: Ellipse, Exercise 1: Exercise 1

Equation of the ellipse, whose focus is $\left(6,7\right)$, directrix is $x+y+2=0$ and $e=\frac{1}{\sqrt{3}}$ is

In an ellipse, the distance between the foci is $8$ and the distance between the directrices is $25$. The length of the major axis is

A man running around a race course notes that the sum of the distances of two flag posts from him is always $10 \mathrm{m}$ and the distance between the flag posts is $8 \mathrm{m}$. The area of the path, he encloses in square metres is

What is the eccentricity of the conic $4x^2+9y^2=144$ $?$

The equation of the ellipse, whose vertices are at $\left(\pm 5,0\right)$ and foci at $\left(\pm 4,0\right)$ is

What is the sum of the major and minor axes of the ellipse, whose eccentricity is $\frac{4}{5}$ and length of latus rectum is $14.4$ units?

What is the equation of the ellipse whose vertices are $(\pm 5,0)$ and foci are at $(\pm 4,0)?$

Let $P$ be a point in the first quadrant lying on the ellipse $9x^2+16y^2=144$, such that the tangent at $P$ to the ellipse is inclined at an angle ${135}^{°}$ to the positive direction of $X$-axis. Then, the coordinates of $P$ are