Conic Sections ...

The equation of the circle in the first quadrature touching each coordinate axis at a distance of one unit from the origin 

The equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x - y + 1 =0 and x = 3 is 

The parametric form of the equation of the circle $${ x }^{ 2 }+{ y }^{ 2 }=9$$ is:

An equilateral triangle is inscribed in the parabola $$y^2=4ax$$ with one vertex at the origin. The radius of the circumcircle of the triangle is 

The equation of a circle with centre at $$(1, -2)$$ and passing through the centre of the given circle $$x^2+y^2+2y-3=0$$, is?

The equation of circle whose centre is $$(1, -3)$$ and which touches the line $$2x-y-4=0$$, is

The latus rectum of a parabola whose focal chord is $$PSQ$$ such that $$SP=3$$ and $$SQ=2$$, is given by 

The length of the latus rectum of the parabola $${ 2y }^{ 2 }+3y+4x-2=0$$ is ________.

The angle between the curves $$x^3-3xy^2=2$$ and $$3x^2y-y^3=2$$ is?

Equation of the ellipse whose minor axis is equal to the distance between foci and whose latus rectum is $$10 ,$$ is given by ____________.