Embibe Experts Solutions for Chapter: Parabola, Exercise 3: Exercise-3

Let $A$ and $B$ be two distinct points on the parabola $y^2=4x$. If the axis of the parabola touches a circle of radius$r$ having $AB$ as its diameter, then the slope of the line joining $A$ and $B$ can be

Let $L$ be normal to the parabola $y^2=4x$. If $L$ passes through the point $\left(9,6\right)$, then $L$ is given by

Let the curve $C$ be the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $A$and $B$ are the points of intersection of $C$ with the line $y=-5$, then the distance between $A$ and $B$ is

If the normals of the parabola $y^2=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x-3{)}^2+(y+2{)}^2=r^2$, then the value of $r^2$ is

Answer $Q.39, Q.40$ and $Q.41$ by appropriately matching the information given in the three columns of the following table.

If a tangent to a suitable conic (Column $1$ ) is found to be $y=x+8$ and its point of contact is $(8,16),$ then which of the following options is the only CORRECT combination?

The slope of the line touching both the parabolas $y^2=4x$ and $x^2=-32y$ is

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is

The radius of a circle having minimum area, which touches the curve $y=4-x^2$ and the lines $y=\left|x\right|,$ is