The vertex of the parabola $x^2 + 4x + 2y - 7 = 0$ is

If the segment intercepted by the parabola $y^2 = 4ax$ with the line $lx + my + n = 0$ subtends a right angle at the vertex,then

The point of contact of the tangent to the parabola $y^2=9x$ which passes through the point $(4, 10)$ and makes an angle $\theta$ with the positive side of the axis of the parabola where $\tan \theta > 2$, is

Find the point of intersection of the parabola $y^2 = 2px$ and a circle whose center is at the focus of the parabola and which touches the directrix of the parabola.

The maximum number of common normals of $y^2=4ax$ and $x^2=4by$ is equal to

The line $y=mx+3$ is tangent to the parabola $y^2=4x$,if the value of $m$ is