Embibe Experts Solutions for Chapter: Parabola, Exercise 2: Exercise-2

Through the vertex '$O$' of the parabola $y^2=4ax$, variable chords $OP$ and $OQ$ are drawn at right angles. If the variable chord $PQ$ intersects the axis of $x$ at $R$, then the distance $OR$ is equal to

From the focus of the parabola, $y^2=8x$ as centre, a circle is described so that a common chord of the curves is equidistant from the vertex & focus of the parabola. Find the equation of the circle.

If from the vertex of a parabola $y^2=4ax$, a pair of chords be drawn at right angles to one another and with these chords as adjacent sides a rectangle be made, locus of the further angle of the rectangle is

If three normal are drawn through $\left(c,0\right)$ to $y^2=4x$ and two of which of perpendicular then the value of $c$ is

Common tangents are drawn to the parabola $y^2=4x$ and the ellipse $3x^2+8y^2=48$ touching the parabola at $A \text{\&} B$ and the ellipse at $C \text{\&} D$, then the area of the quadrilateral $ABCD$ is $\lambda \sqrt{2}$ then $\lambda$ is equal to

Let tangent at point $AB$ and vertex $\left(V\right)$ of parabola is$x-2 y+1=0,3 x+y+4=0$ and $y=x$ respectively. If focus of parabola is $\left(\frac{a}{7},\frac{b}{7}\right)$ then find the value of $(a+5 b).$

Locus of the centre of the circle passing through the vertex and the mid-points of perpendicular chords from the vertex of the parabola $y^2=4ax$ is.

Two confocal parabola intersect at $A$ and $B$. If their axis are parallel to $x$-axis and $y$-axis respectively, then slope of chord $AB$ can be :