Conic Sections ...

Find the equation of a circle whose centre is (2, - 1 ) an radius is 3

In what ratio, the point of intersection of the common tangents to hyperbola $$\dfrac{x^2}{1}-\dfrac{y^2}{8}=1$$ and parabola $$y^2=12x$$, divides the foci of the given hyperbola?

$$AB$$ is a chord of the circle $$x^{2} + y^{2} = 9$$. The tangent at $$A$$ and $$B$$ intersect at $$C$$. If $$(1, 2)$$ is the midpoint of $$AB$$, the area of $$\triangle ABC$$ is (in square units).

The equation $$\dfrac {x^{2}}{2 - \lambda} + \dfrac {y^{2}}{\lambda - 5} - 1 = 0$$ represents an ellipse, if

The eccentricity of the ellipse $$9x^{2} + 25y^{2} - 18x - 100y - 116 = 0$$, is

The eccentricity of the ellipse $$5x^{2} + 9y^{2} = 1$$ is

An ellipse has its centre at $$(1, -1)$$ and semi-major axis $$= 8$$ and it passes through the point $$(1, 3)$$. The equation of the ellipse is

The eccentricity of the ellipse $$25x^{2} + 16^{2} = 400$$ is

If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to

If the latus-rectum of an ellipse is one half of its minor axis, then its eccentricity is