Conic Sections ...

The centre, vertex, focus of a conic are $$(0,0),
(0,5), (0,6)$$. Its length of latus rectum is

The total number of real tangents that can be drawn to the ellipse $$3x^{2}+5y^{2}=32$$ and $$25x^{2}+9y^{2}=450$$ passing through $$(3,5)$$ is

The length of the latus rectum of the hyperbola $$x^{2}-4y^{2}=4$$ is

A straight line is drawn through the centre of the circle $${x}^{2}+{y}^{2}=2ax$$ parallel to $${x}+2y=0$$ and intersecting the circle at $${A}$$ and $${B}$$. Then, the area of $$\Delta A{O}{B}$$ is

The equation  $$\sqrt{(x-2)^{2}+y^{2}}+\sqrt{(x+2)^{2}+y^{2}}=5$$ represents

The length of latus rectum of the hyperbola $$4x^{2}-9y^{2}-16x-54y-101=0$$ is

The equation $$(\mathrm{x}^{2}-\mathrm{a}^{2})^{2}+(\mathrm{y}^{2}-\mathrm{b}^{2})^{2}=0$$ represent points which are

The equation of directrix and latus rectum of a parabola are $$3x-4y+27=0$$ and $$3x-4y+2=0$$. Then the length of latus rectum is

A circle of radius $$5$$ units passes through the points $$(7,1),(9,5)$$. If the ordinate of the centre is less than $$2$$, then the equation of the circle is

A parabola with axis parallel to $$x$$ axis passes through $$(0, 0), (2, 1), (4, -1).$$ Its length of latus rectum is