Embibe Experts Solutions for Chapter: Parabola, Exercise 1: KEAM 2018

The equation $a{x}^2+4xy+y^2+ax+3y+2=0$ represents a parabola if $a$ is

The vertex of the parabola $\mathrm{y}={\mathrm{x}}^2-2\mathrm{x}+4$ is shifted $\mathrm{p}$ units to the right and then $\mathrm{q}$ units up. If the resulting point is $(4,5),$ then the values of $\mathrm{p}$ and $\mathrm{q}$ respectively are

The vertex of the parabola $\mathrm{y}=(\mathrm{x}-2)(\mathrm{x}-8)+7$ is

The length of the Latus rectum of the parabola $x=a{y}^2+by+c$ is

The focus of the parabola $y^2-4y-x+3=0$ is

The focus of the parabola ${\left(y+1\right)}^2=-8\left(x+2\right)$ is

The line $\mathrm{y}=\mathrm{mx}+2$ intersects the parabola $\mathrm{y}={\mathrm{ax}}^2+5\mathrm{x}-2$ at $(1,5)$. Then the value of $\mathrm{a}+\mathrm{m}$ is equal to

The condition that the straight line $lx+my+n=0$ touches the parabola $x^2=4ay$ is