Conic Sections ...

The eq. of the circle which touches the exes of y at a distance of $$4$$ from the origin and cuts the intercepts of $$6$$ units from the axis of x is

$$AB$$ is a diameter of $$x^{2}+9y^{2}=25$$. The eccentric angle of $$A$$ is $$\dfrac{\pi}{6}$$. Then the eccentric angle of $$B$$ is

Let $$P,\ Q,\ R,\ S$$ be the feet of perpendicular drawn from the point $$(1,\ 1)$$ the lines $$y=3x+4$$ and $$y=-3x+6$$ and their angle bisectors respectively, the equation of the circle whose extremities of a diameter are $$R$$ and $$S$$ is 

The length of the latus rectum of the parabola whose focus is (3,0) and directrix is 3x-4y-2=0 is

The area bounded by the parabola $${ y }^{ 2 }=4xy\quad $$ and its rectum is :-

A parabola passing through the point $$(-4,-2)$$ has its vertex at the origin and $$y-$$axis as its axis. The latus rectum of the parabola is

The equation of the latusrectum of the parabola $${ x }^{ 2 }+4x+2y=0$$ is:-

The equation of the circle having as a diameter, the chord $$x - y - 1 = 0$$ of the circle $$2x^2 + 2y^2 - 2x - 6y - 25 = 0$$, is

The curve represented by $$Rs \left(\dfrac{1}{z}\right)=C$$ is (where $$C$$ is a constant and $$\neq 0$$)

The intercept on the line $$y = x$$ by the circle $${x^2} + {y^2} - 2x = 0$$ is $$AB$$. The equation of the circle with $$AB$$ as a diameter, is