List of top Mathematics Questions on Parabola

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 ...

An equilateral triangle OAB is inscribed in the parabola $y^2 = 4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

Let the parabola \( y = x^2 + px + q \) passing through the point \( (1, -1) \) be such that the distance between its vertex and the x-axis is minimum. Then the value of \( p^2 + q^2 \) is:

The normal drawn to the parabola \[ y^2=8x \] at \((2,4)\) meets the parabola again at the point

If \(a\neq 0\) and the line \[ 2bx+3cy+4d=0 \] passes through the points of intersection of the parabolas \[ y^2=4ax \] and \[ x^2=4ay, \] then

Let \(O\) and \(S\) be the vertex and focus of the parabola \[ y^2=4ax \] respectively and \(x=k\) be its double ordinate of length \(2\sqrt6\,a\). If the line \(x=k\) cuts the \(X\)-axis at \(P\), then the length of the double ordinate drawn through \(O\) to the parabola having \(P\) and \(S\) as vertex and focus is

For parabola \(y^2=5x\), normal at P meets x-axis at Q. If PQ subtends \(60^\circ\) at vertex, slope of normal is

Common tangent to circle \(x^2+y^2=4\) and parabola \(y^2=8\sqrt2 x\) is \(y=mx+c\). Then \(\sqrt{m+c^2}=\)

If \(P(t_1)\) and \(Q(t_2)\) are two points on the parabola \[ y^2=7x \] If \(t_1=2\) and \(t_2=-4\), then the length of chord \(PQ\) is

If \(\theta\) is angle between parabolas \[ y^2=108x \] and \[ x^2=32y \] then \[ \cos2\theta= \]

If the nearest point on the parabola $y^{2}=4x$ to the given point $P(-1,4)$ is $Q(h,k)$ and $PQ=d$, then $h^{2}+k^{2}+d^{2}=$}

If a straight line \[ y=mx+c \] touches the circle \[ x^2+y^2=4 \] and parabola \[ y^2=4x \] then \(2m^2=\)

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 .....

PSQ is a focal chord of the parabola \[ y^2=12x. \] \(A\) and \(B\) are respectively the feet of the perpendiculars drawn from \(P\) and \(Q\) on the directrix of the parabola. If the length of \(AB\) is \(7\sqrt3\) and \[ P=(3t^2,6t), \qquad (0<t<1), \] then \(t=\)