Embibe Experts Solutions for Chapter: Parabola, Exercise 2: Level 2

If $a{x}^2+2hxy+b{y}^2-82x+98y+144=0$ is the equation of a parabola with focus $(2, -3)$ and directrix $3x-2y+5=0,$ then $a{x}^2+2hxy+b{y}^2=0$ represents

The shortest distance between the line $x-y=1$ and the curve $x^2=2y$ is:

Two tangents are drawn from $\left(p,q\right)$ to the parabola $y^2=8x$ such that the slope of one of the tangent is thrice of the other, then $\frac{3q^2}{p}=$

A line is a common tangent to the circle ${\left(x-3\right)}^2+y^2=9$ and the parabola $y^2=4x$. If the two points of contact $\left(a,b\right)$ and $\left(c,d\right)$ are distinct and lie in the first quadrant, then $2\left(a+c\right)$ is equal to ___ .

Let $P, Q$ be the points with parameters $t_1, t_2$ on the parabola $y^2=4ax.$ If the normals at $P, Q$ meet on the parabola at $R\left(t_3\right),$ then

The equation of common normal to the circle $x^2+y^2-12x+16=0$ and parabola $y^2=4x$ is

Normals at $A,B,C$ are drawn to $y^2=4x$ which intersects at $P\left(3,0\right)$. Then the equation of circumcircle of $\Delta ABC$ is

If $L$ is the minimum distance between the curves ${\left(x-6\right)}^2+y^2=5$ and $y^2=4x$, then the value of $L^2$ is