Embibe Experts Solutions for Exercise 1: Telangana Board-2018

Find the equation of the parabola whose vertex is $\left(3,-2\right)$ and focus is $\left(3,1\right)$.

Derive the equation of parabola in the standard form, that is $y^2=4ax$.

Find the equation of the normal to the parabola $y^2=4x$ which is parallel to $y-2x+5=0.$

From an external point '$P$' tangents are drawn to the parabola $y^2=4ax$ and these tangents make angles ${\theta }_1$ and ${\theta }_2$ with its axis, such that $\cot {\theta }_1+\cot {\theta }_2$ is a constant '$d$'. Then, show that $P$ lie on a horizontal line.

Find the equation of the tangent to the parabola $y^2=6x$ at the positive end of the latus rectum.

Derive the equation of a parabola in standard form.