Conic Sections ...

The equation of hyperbola whose coordinates of the foci are $$(\pm8,0)$$ and the lenght of latus rectum is $$24$$ units, is

The lines $$2x - 3y - 5 = 0$$ and $$3x -4y = 7$$ are diameters of a circle of area 154 sq units, then the equation of the circle is.( Use $$\pi = \dfrac{22}{7}$$)

Let $$ABCD$$ be a square of side length $$1$$. and $$\Gamma $$ a circle passing through $$B$$ and $$C$$, and touching $$AD$$. The radius of $$\Gamma $$ is

Consider the parametric equation
$$x = \dfrac {a(1 - t^{2})}{1 + t^{2}}, y = \dfrac {2at}{1 + t^{2}}$$.

What is the radius of the circle passing through the point $$(2, 4)$$ and having centre at the intersection of the lines $$x - y = 4$$ and $$2x + 3y + 7 = 0$$?

The differential equation $$(3x + 4y + 1)dx + (4x + 5y + 1) dy = 0$$ represents a family of

The line $$(x-2)\cos \theta +(y-2)\sin \theta =1$$ touches a circle for all value of $$\theta$$, then the equation of circle is

The latus rectum of the ellipse is half the minor axis. Then its eccentricity is

The equation of the smallest circle passing through the points $$(2, 2)$$ and $$(3, 3)$$ is

If focii of $$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$$ coincide with the focii of $$\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$$ and eccentricity of the hyperbola is $$2$$, then