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

Equation of parabola having the extremities of its latus rectum as $\left(3,4\right)$ and $\left(4,3\right)$ is

If $P$, $Q$ and $R$ are three points on parabola $y^2=4x$ and normal at $P$ and $R$ meet at $Q$, then the locus of midpoint of the chord $PR$ is a parabola whose vertex is at

If the normals to the parabola $y^2=4ax$ at three points $P, Q$ and $R$ meet at $A$ and $S$ be the focus, then $SP·SQ·SR$ is equal to

If the normal at three points $P,Q,R$ of the parabola $y^2=4ax$ meet in a point $O$ and $S$ be its focus, then $\left|SP\right|·\left|SQ\right|·\left|SR\right|$ is equal to

If $\left(x_1,y_1\right), \left(x_2,y_2\right)$ and $\left(x_3,y_3\right)$ are the feet of the three normals drawn from a point to the parabola $y^2=4ax,$ then $\frac{x_1-x_2}{y_3}+\frac{x_2-x_3}{y_1}+\frac{x_3-x_1}{y_2}$ is equal to

The focal distance of a point on the parabola $y^2=16x$ whose ordinate is twice the abscissa is (except the vertex of parabola)

The radius of circle which passes through the focus of the parabola $x^2=4y \&$ touches it at the point $\left(6, 9\right)$ is $a\sqrt{10},$ then value of $\text{'}a\text{'}$ is

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 ___ .