Embibe Experts Solutions for Chapter: Parabola, Exercise 1: Exercise 1

The coordinates of the focus of the parabola described parametrically by $x=5t^2+2,y=$$10t+4$ (where $t$ is a parameter) are

 Locus of the intersection of the tangents at the ends of the normal chords of the parabola  $y^2=4ax$  is - 

If $a{x}^2+2hxy+b{y}^2-82x+98y+144=0$ is the equation of a parabola with focus $(2, -3)$ and directrix $3x-2y+5=0,$ then $a{x}^2+2hxy+b{y}^2=0$ represents

The equation of common normal to the circle $x^2+y^2-12x+16=0$ and parabola $y^2=4x$ is

If one end of a focal chord of the parabola $y^2=4x$ is $(1,2)$, the other end doesn't lie on 

Identify the following statements for true/false (T/F) in order
$S1:$The tangents at the extremities of a focal chord of a parabola are perpendicular
$S2:$ The tangents at the extremities of a focal chord of a parabola are parallel
$S3:$The tangents at the extremities of a focal chord of a parabola intersect on the directrix

$\mathrm{S}4$ : The tangents at the extremities of a focal chord of a parabola intersect at the vertex

The equation of common tangent of $x^2+y^2=2$ and $y^2=8x$ is

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