Amit M Agarwal Solutions for Chapter: Parabola, Exercise 5: Entrances Gallery

Let $P$ and $Q$ be the points on the parabola $y^2=4x,$ so that the line segment $PQ$ subtends right angle at the vertex. If $PQ$ intersects the axis of the parabola at $R$ then the distance of the vertex from $R$ is

If the straight lines $y=\pm x$ intersect the parabola $y^2=8x$ in points $P$ and $Q,$ then the length of $PQ$ is

The sum of the reciprocals of focal distances of a focal chord $PQ$ of $y^2=4ax$ is

The distance between the vertex of the parabola $y=x^2-4x+3$ and the centre of the circle $x^2=9-{\left(y-3\right)}^2,$ is

The parabola $y^2=4x$ and the circle $x^2+y^2-6x+1=0$ will

The equation of tangent of $y^2=12x$ and making an angle $\frac{\pi }{3}$ with the $X$-axis, is

If $t_1$ and $t_2$ are the parameters of the endpoints of a focal chord for the parabola $y^2=4ax,$ then which one is correct?

One of the points on the parabola $y^2=12x$ with focal distance $12,$ is