Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of the ellipse x² + 9y² = 9, then the ratio of a² : b² equals to

Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ on the line bx $$-$$ ay = 0 and let C be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of SP and CP is

The line segment joining the foci of the hyperbola $${x^2} - {y^2} + 1 = 0$$ is one of the diameters of a circle. The equation of the circle is

Let A($$-$$ 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $$\angle MBA$$ = 2$$\angle MAB$$. Then, the point M moves along