List of top Mathematics Questions on Parabola asked in MHT CET

The equation of the common tangent to the parabolas \(y^{2}=4x\) and \(x^{2}=32y\) is ...

The equation of the line tangent to the curve \(y^{2}=4x\) with an inclination of \(60^{\circ }\) is:

The area (in sq.units) of a triangle formed by joining the vertex and the endpoints of the latus rectum of the parabola \(x^{2}=-20y\) is...

The equation of the directrix of the parabola \(x^{2}-4x-5y-1=0\) is...

One of the tangents at the end of the latus rectum of the parabola \(y^{2}=12x\) is

The tangent to the parabola \(x^{2}=2y\) at point P makes an angle of \(45^{\circ }\) with the X-axis, then the coordinates of P are:

If the tangent to the curve \(y^{2}=4x\) at \((4,4)\) touches the circle \(x^{2}+y^{2}-c=0\) then the value of \(5c\) is

The area of the triangle formed by the vertex and the endpoints of the latus rectum of the parabola \(x^{2}=-18y\) is ...

A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If \(P(α,4)\) 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 is

In \(△ABC\), with usual notation, if cot A, cot B, cot C are in arithmetic progression, then

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 distance of the focus of the parabola \(y^2 = 16x\) from its directrix 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 angle between the tangents drawn from the point (1, 4) to the parabola $y^2 = 4x$, is ______.

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

Angle between the parabola \[ y^2 = 4(x - 1) \quad \text{and} \quad x^2 + 4(y - 3) = 0 \quad \text{at the common end of their latus rectum is} \]

If the lines \(\frac{x-1}{2} = \frac{y+1}{k} = \frac{z}{2}\) and \(\frac{x+1}{5} = \frac{y+1}{2} = \frac{z}{k}\) are coplanar, then the equation of the plane containing these lines are

Find the area of the region bounded by the parabola $$ y^2 = 4ax \text{ and its latus rectum.} $$