G Tewani Solutions for Chapter: Parabola, Exercise 3: DPP

If $BC$ is a latus rectum of the parabola $y^2=4ax$ and $A$ is the vertex, then the minimum length of the projection of $BC$ on a tangent drawn in the portion $BAC$ is

Through the vertex $O$ of the parabola $y^2=4ax$, $a>0$, a perpendicular is drawn to any tangent, meeting it at $P$ and the parabola at $Q$. Then $OP, 2a$ and $OQ$ are in

Tangents $PQ$ and $PR$ are drawn to the parabolas $y^2=20\left(x+5\right)$ and $y^2=60\left(x+15\right)$ respectively, such that $\angle RPQ=\frac{\pi }{2}$. Then the locus of point $P$

The locus of the centroid of a triangle formed by a tangent to the parabola $y^2=36x$ with the coordinate axes, is

$PC$ is the normal at $P$ to the parabola $y^2=4ax, C$ being on the axis. $CP$ is produced outwards to $Q$ so that $PQ=CP$. The locus of $Q$ is a parabola that has focus

If the parabolas $y^2=4kx \left(k>0\right)$ and $y^2=4\left(x-1\right)$ do not have a common normal other than the axis of parabola, then $k\in$

At a point $P$ on the parabola $y^2=4ax$, a tangent and normal are drawn. Tangent intersects the $x$-axis at $Q$ and normal intersects the curve at $R$ such that chord $PR$ subtends an angle of ${90}^{\mathrm{o}}$ at its vertex. Then

Let $y^2-5y+3x+k=0$ be a parabola, then