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

If $\text{'}m\text{'}$ varies and range of $c$ for which the line $y=mx+c$ touches the parabola $y^2=8\left(x+2\right)$ is $R-\left(-\lambda , \lambda \right),$ then value of $\lambda$ is equal to

Two tangents to the parabola $y^2=8x$ meet the tangent at its vertex in the points $P \& Q.$ If $PQ=4$ units and the locus of the point of the intersection of the two tangents is $y^2=\lambda \left(x+2\right),$ then value of $\frac{10}{\lambda }$ is

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

In the parabola $y^2=4ax,$ the tangent at the point $P,$ whose abscissa is equal to the latus rectum meets the axis in $T \&$ the normal at $P$ cuts the parabola again at $Q.$ If $PT\mathit{:}PQ\mathit{=}a\mathit{:}b$ (where $a$ and $b$ are relative prime), then find value of $\left(\frac{b}{a}\right)$.

If the locus of a point, such that two of the three normals drawn from it to the parabola $y^2=4ax$ are perpendicular is $y^2=a\left(x-\lambda a\right),$ then value of $\lambda$ is

If the normal at $P\left(18, 12\right)$ to the parabola $y^2=8x$ cuts it again at $Q$, if $PQ=\frac{80\sqrt{10}}{\lambda },$ then value of $\lambda$ is