Conic Sections ...

if the lines $$ 3x-4y-7=0$$ and $$2x-3y-5=0$$ are two diameter of a circle of area $$49\pi$$ square units the equation of the circle is

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point $$ (-3,1)$$ and has eccentricity $$\sqrt {\frac{2}{5}} $$ is 

The name of the conic represented by $$\sqrt{\dfrac{x}{a}}+\sqrt{\dfrac{y}{b}}=1$$ is

The equation of the tangent to the ellipse such that sum of perpendiculars dropped from foci is 2 units, is

$$(a, c)$$ and $$(b, c)$$ are the centres of two circles whose radical axis is the y-axis. If the radius of first circle is $$r$$ then the diameter of the other circle is 

The equation of the latus rectum of the hyperbola $$\dfrac{(x-4)^2}{16}-\dfrac{(y-3)^2}{20}=1$$ are?

$${x^2} - {y^2} + 5x + 8y - 4 = 0$$

Equation of circle having centre $$(5, 2)$$ and which passes through the point $$(1, -1)$$ is?

S and S' foci of an ellipse. B is one end of the minor axis. If $$\angle{SBS'}$$ is a right angled isosceles triangle, then e$$=?$$

The latusrectum of a parabola $$y^{2}=4ax$$ whose focal chord is $$PSQ$$ such that $$SP=3$$ and $$SQ=2$$, is given by