If the line $7y - 4x = 10$ is a tangent to the parabola $y^2 = 4x$,find the point of contact.

The locus of the midpoint of the focal radii of a variable point moving on the parabola $y^2 = 4ax$ is a parabola whose:

For the parabola $y^2 = 4ax$,what is the $x$-coordinate of the point closest to the focus?

The point on the curve $y^2=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$ is

If $Q$ is the point on the parabola $y^2=4x$ that is nearest to the point $P(2,0)$,then $PQ=$

Let the focal chord $PQ$ of the parabola $y^2=4x$ make an angle of $60^{\circ}$ with the positive $x$-axis,where $P$ lies in the first quadrant. If the circle,whose one diameter is $PS$,$S$ being the focus of the parabola,touches the $y$-axis at the point $(0, \alpha)$,then $5 \alpha^2$ is equal to :