G Tewani Solutions for Chapter: Parabola, Exercise 4: DPP

Let $TP$ and $TQ$ be any two tangents to a parabola and the tangent at a third point $R$ cuts them in $P^{\text{'}}$ and $Q^{\text{'}}$. Then the value of $\frac{T{P}^{\text{'}}}{TP}+\frac{T{Q}^{\text{'}}}{TQ}$ must be

The distance of two points $P$ and $Q$ on the parabola $y^2=4ax$ from the focus $S$ are $3$ units and $12$ units, respectively. The distance of the point of intersection of the tangents at $P$ and $Q$ from the focus $S$ is

A parabola having directrix $x+y+2=0$ touches a line $2x+y-5=0$ at $(2,1)$. Then the semi-latus rectum of the parabola is

Let $A, B$ and $C$ be three distinct points on $y^2=8x$ such that normals at these points are concurrent at $P$. The slope of $AB$ is $2$ and abscissa of centroid of $\mathit{△}ABC$ is $\frac{4}{3}$. Which of the following is (are) correct?

If $PQ$ and $RS$ are normal chords of the parabola $y^2=8x$ at $P \& R$, respectively, and the points $P, Q, R$ and $S$ are concyclic, then

Tangents are drawn from $P\left(-2, 0\right)$ to $y^2=8x$. Radius of circle(s) that would touch these tangents and the corresponding chord of contact can be equal to

Given a parabola $y^2=4ax$ and the points $A\left(a{t}^2, 2at\right), B\left(a{t}^{-2}, -2a{t}^{-1}\right), C\left(\frac{4a}{t^2}, \frac{4a}{t}\right)$ and $D\left(a{\left(t+\frac{2}{t}\right)}^2, -2a\left(t+\frac{2}{t}\right)\right)$, choose all the correct alternatives.

If a parabola touches the lines $y=x$ and $y=-x$ at $P\left(3, 3\right)$ and $Q\left(2, -2\right)$ respectively, then