Subject Experts Solutions for Chapter: Conic Section, Exercise 1: Practice Exercise

A point $P$ moves such that its distances from $\left(1,2\right)$ and $\left(-2,3\right)$ are equal. Then the locus of $P$ 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 parabola, whose vertex is at $\left(0,0\right)$ and focus is at $\left(0,-2\right)$?

What is the length of the latus rectum of an ellipse $25x^2+16y^2=400$ $?$

The point on the parabola $y^2=4ax$ nearest to focus has its abscissa

The hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passes through the point $\left(3\sqrt{5},1\right)$ and the length of its latus rectum is $\frac{4}{3}$ units. The length of the conjugate axis is

Consider any point $P$ on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$, in the first quadrant. Let $r$ and $s$ represent its distances from $\left(4,0\right)$ and $\left(-4,0\right)$, respectively, $\left(r+s\right)$ is equal to

The eccentricity of the hyperbola $16x^2-9y^2=1$ is