Tag: mathematics and statistics

The locus of the midpoint of the line segment joining the focus to a  moving point on the parabola y$^2$ - 4ax is another parabola with directrix

Equation of the directrix of the parabola $4y^2-6x-4y-5=0$ is 

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

The focus of the parabola $x^2 -4x+2y+8=0$ is 

The equation of the directrix of the parabolas $x=-2at,\ y=-at^{2},\ t\ \epsilon \ R$ is

The angle of intersection at the origin to the curves ${ y }^{ 2 }=4x$ and ${ x }^{ 2 }=4y$ is :

if the vertex and the focus of the parabola are $(-1, -1) & (2, 3)$ respectively, then the equation of the directrix is

The parametric equation of a parabola is $x=t^{2}+1, y=2t+1$. The Cartesian equation of its directrix is 

$TP$ and $TQ$ are tangents to parabola $y^{2}=4x$ and normal at $P$ and $Q$ intersect at a point $R$ on the curve. The locus of the center of the circle circumscribing $\Delta TPQ$ is parabola whose

For parabola $x^{ 2 } + y^{ 2 } + 2xy 6x 2y + 3 = 0$ the focus is