If the slope of one of the two lines given by $\dfrac{x^2}{a} + \dfrac{2xy}{h} + \dfrac{y^2}{b} = 0$ is twice that of the other, then $h^2 : ab = $ ...

If the equation $3x^2 + (3 - p)xy + qy^2 - 2px = 8pq$ represents a circle, then the area (in sq. units) of this circle is

The ellipse $4x^2 + 9y^2 = 1$ intersects positive Y-axis at point A. If S and S' are its foci, then the area (in sq. units) of $\Delta SAS'$ is _____

$\lim_{x \to 1} \left[\dfrac{x-2}{x^2-x} - \dfrac{1}{x^3 - 3x^2 + 2x}\right] = $