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

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

The eccentricity $e$ of an ellipse satisfies the condition

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

The length of latus rectum of the ellipse $4x^2+9y^2=36$ 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 length of the latus rectum of an ellipse $25x^2+16y^2=400$ $?$

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

Let $L$ be a common tangent line to the curves $4x^2+9y^2=36$ and ${\left(2x\right)}^2+{\left(2y\right)}^2=31$. Then the square of the slope of the line $L$ is ______.