EXERCISE-1

If $M$ is the foot of the perpendicular from a point $P$ of a parabola $y^2=4ax$ to its directrix and $SPM$ is an equilateral triangle, where $S$ is the focus, then $SM$ is equal to -

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 distance $OR$ :

Point $P$ lies on $y^2=4ax \& N$ is foot of perpendicular from $P$ on its axis. A straight line is drawn parallel to the axis to bisect $NP$ and meets the curve in $Q$. $NQ$ meets the tangent at the vertex in a point $T$ such that $AT=kNP,$ then the value of $k$ is : (where $A$ is the vertex)

 The tangents to the parabola  $x=y^2+c$  from origin are perpendicular then $c$ is equal to - 

The locus of a point such that two tangents drawn from it to the parabola $y^2=4ax$ are such that the slope of one is double the other is -

The equation of the circle drawn with the focus of the parabola $(x-1{)}^2-8y=0$ as its centre and touching the parabola at its vertex is :

Tangents are drawn from the point $\left(-1,2\right)$ on the parabola$y^2=4x$ . The length, these tangents will intercept on the line $x=2$:

 Locus of the point of intersection of the perpendiculars tangent of the curve  $y^2+4y-6x-2=0$  is :