Amit M Agarwal Solutions for Chapter: Parabola, Exercise 4: Target Exercises

Tangent and normal drawn to parabola at $A\left(a{t}^2, 2at\right), t\ne 0,$ meet $X$ -axis at points $B$ and $D$ respectively. If the rectangle $ABCD$ is completed, then the locus of $C$ is

Normals $PO, PA$ and $PB, O$ being the origin, are drawn to $y^2=4x$ from $P\left(h,0\right).$ If $\angle AOB=\frac{\pi }{2},$ then area of quadrilateral $OAPB$ is equal to

The radius of the circle whose centre is$(-4, 0)$ and which cuts the parabola $y^2=8x$ at $A$ and $B$, such that its common chord $AB$ subtends a right angle at the vertex of the parabola is equal to

If the line $y=mx+1$ is a tangent to $y^2=4mx,$ then the distance of this tangent from the parallel normal is

$AB$ is a double ordinate of the parabola $y^2=4ax.$ Tangents drawn to parabola at $A$ and $B$ meets $Y$-axis at $A_1$ and $B_1,$ respectively. If the area of trapezium $A{A}_1{B}_{1}B$ is equal to $24a^2,$ then the angle subtended by $A_1{B}_1$ at the focus of parabola is equal to

Maximum number of common normals of $y^2=4ax$ and $x^2=4by$ can be equal to

If two different tangents of $y^2=4x$ are the normals to $x^2=4by,$ then

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