Conic Sections ...

Length of the latusrectum of the hyperbola $$xy=c$$ ,is equal to

The length of the latus rectum of the parabola, whose focus is $$\left(\displaystyle \frac{u^{2}}{2g}\sin 2\alpha,\frac{-u^{2}}{2g}\cos 2\alpha \right)$$ and directrix is $$y=\dfrac{u^{2}}{2g}$$, is

A parabola has x- axis as its axis, y- axis as its directrix and $$4a$$ as its latus rectum. If the focus lies to the left side of the directrix then the equation of the parabola is

If $$L_{1}L_{2}$$ is the latusrectum of $$y^{2}=12x$$,  $$P$$ is any point on the directrix then the area of $$\Delta PL_{1}L_{2}$$ =

The length of latus rectum of the parabola $$(x-2a)^{2}+y^{2}=x^{2}$$ is

The arrangement of the following parabolas in the ascending order of their length of latusrectum 
A)   $$y=4x^{2}+x+1$$     B) $$2y=x^{2}+x+5$$
C)   $$x=2y^{2}+y+3$$     D) $$y^{2}+x+y+9=0$$

The length of latus rectum of the parabola $$y^{2}+8x-2y+17=0$$ is

The length of latus rectum of the hyperbola $$xy-3x-3y+7=0$$ is

The equation of the circle having centre $$(1,\ -2)$$ and passing through the point of intersection of the lines $$3x+y=14$$ and $$2x+5y=18$$ is