Conic Sections ...

The equation of parabola whose latus rectum is $$2$$ units, axis is $$x+y-2=0$$ and tangent at the vertex is $$x-y+4=0$$ is given by

If major axis is the x-axis and passes through the points $$(4, 3)$$ and $$(6, 2)$$, then the equation for the ellipse whose centre is the origin is satisfies the given condition.

$$(4-\mathrm{a})\mathrm{x}^{2}+(12-\mathrm{a})\mathrm{y}^{2}=\mathrm{a}^{2}-16\mathrm{a}+48$$ represents an ellipse. Then:

Latus rectum of a parabola is a ........ line segment with respect to the axis of the parabola through the focus whose endpoints lie on the parabola.

If the equation of the incircle of an equilateral triangle is $${ x }^{ 2 }+{ y }^{ 2 }+4x-6y+4=0$$, then the equation of the circumcircle of the triangle is

The length of the latus rectum of the parabola 
$$169\left \{ (x-1)^{2}+(y-3)^{2} \right \}=(5x-12y+17)^{2}$$ is

The equation $$x^{2}+y^{2}-2x+4y+5=0$$ represents 

The equation $$7y^2-9x^2+54x-28y-116=0$$ represents

If the parabola $$y^{2}=4ax$$ passes through $$(3,\:2)$$ then the length of latus rectum is

The equation of the circle passing through the point $$(1, 1)$$ and having two diameters along the pair of lines $$x^{2}-y^{2}-2x+4y-3=0$$ is