Parabola

A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If $P(\alpha , 4)$ is a point on this parabola such that the tangent to the parabola at point P passes through the origin, then the distance of P from origin i...

The equation of the common tangent touching the circle $(x-3)^2 + y^2 = 9$ and the parabola $y^2 = 4x$ above the X-axis is

The area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 48y$ to the ends of its latus rectum, is .....

The distance of the focus of the parabola $y^2 = 16x$ from its directrix is...

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4 x$, is

The equation of the directrix of the parabola $y^2+4 y+4 x+2=0$ is

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

The Y-intercept of the common tangent to the parabolas $y^2=32 x$ and $x^2=108 y$ is

Angle between the parabola $y^2=4(x-1)$ and $x^2+4(y-3)=0$ at the common end of their latus rectum is

The area of the triangle formed by the lines joining the vertex of the parabola $x^2=20 y$ to the end of its latus rectum is

The equation of the tangent to the parabola $y^2=8 x$, which is parallel to the line $4 x-y+3=0$ is

The area of the triangle formed by the lines joining vertex of the parabola $x^2=12 y$ to the extremities of its latus rectum is

The equation of the directrix of the parabola $3 x^2=16 y$ is

The cartesian co-ordinates of the point on the parabola \(y^2=x\) whose parameter is \(-\frac{4}{3}\) are

The length of latus-rectum of the parabola \(x^2+2 y=8 x-7\) is