Amit M Agarwal Solutions for Chapter: Parabola, Exercise 3: Work Book Exercise 14.3

The chord of contact of the pair of tangents drawn from each point on the line $2x+y=4$ to the parabola $y^2=-4x$ pass through the point

The inclination of the normal with positive direction of $X$-axis, drawn at another end of a normal to the parabola $y^2=4x$ is always

Two parabolas with the same axis, focus of each being exterior to the other and the latus rectum being $4a$ and $4b$. The locus of middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a/an

The set of real values of $a$ for which at least one tangent to $y^2=4ax$ becomes normal to the circle $x^2+y^2-2ax-4ay+3a^2=0$

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 $\left(x_1,y_1\right), \left(x_2,y_2\right)$ 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