Parabola

A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c. The locus of P is a

Two tangents to the parabola $y^2=4ax$ make angles ${\alpha }_1$and ${\alpha }_2$ with the x-axis. The locus of their point of intersection if $\frac{cot {\alpha }_1}{cot {\alpha }_2}=2$is

If the Cartesian co-ordinates of the point on the parabola ${\mathrm{y}}^2=12\mathrm{x}$ whose parameter is $2$ is $\left(p,q\right) \mathrm{then} p+q=$

The length of latus-rectum of following parabola:$x^2=-10y$ is 

The length of latus-rectum of following parabola: $y^2=-12x$ is 

The equation of parabola with vertex at origin,passing through the point $\left(2,3\right)$ and axis of parabola is along x-axis is $y^2=\frac{a}{b}x$, then find $a+b$.

The equation of parabola with vertex at origin and having Directrix as $y-2=0$ is 

The equation of parabola with vertex at origin and having focus at $\left(-4,0\right)$ is 

If the parabola $y^2=4px$ passes through the point $\left(3,-2\right)$, then find the length of latus-rectum.

The length of latus-rectum of the conic represented by the equation $y^2=2\sqrt{3}x$ is 

The equation of the directrix of the parabola $y^2=8\sqrt{3}x$ is $x+l\sqrt{m}$, then find $l-m$.

The equation of parabola having focus at $\left(1,1\right)$ and directrix as $3x+4y-2=0$ is 

The co-ordinates of focus of the following parabola :$x^2=-9y$ is 

If the co-ordinates of focus of the following parabola :$y^2=12x$ is $\left(l,m\right)$, then find $l+m$.

The equation of a parabola is $x^2+y^2-2xy-8x+20y+k=0$. If the equation of directrix of parabola is $x+y=2$ and the focus is $\left(3,-4\right)$, then find the value of $k$.

The equation of the parabola with vertex at the origin, the axis along $Y$-axis, and passing through the point $\left(-10,-5\right)$ is 

The area of the triangle formed by the tangents at $\left(x_1,y_1\right), \left(x_2,y_2\right)$and $\left(x_3,y_3\right)$ to the parabola $y^2=4ax(a>0)$ is

Equation of parabola whose vertex is $(3,-2)$ and focus is $(3,1)$

The focal distance of the point $\left(4,4\right)$ on the parabola with vertex at $\left(0,0\right)$ and symmetric about $y$-axis is

The locus of a point, which moves so that its distance from a fixed line not passing through center of circle is equal to the length of the tangent drawn from it to a given circle, is a parabola. Its directrix is $lax=m{a}^2+n{r}^2$. Find $l-m+n$.