The distance of the point $'\theta '$on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ from a focus is

A common tangent to $9x^2 + 16y^2 = 144 ; y^2 – x + 4 = 0 \,\,\&\,\, x^2 + y^2 – 12x + 32 = 0$ is :

A tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}}$ + $\frac{{{y^2}}}{{32}}$ $= 1$  intersects the major and minor axes in points $A$ and $ B$  respectively. If $C$  is the centre of the ellipse then the area of the triangle $ ABC$  is : ………….. $\mathrm{sq. \,units}$

If the distance between the foci of an ellipse is $6$ and the distance between its directrices is $12$, then the length of its latus rectum is

The equation of tangent and normal at point $(3, -2)$ of ellipse $4{x^2} + 9{y^2} = 36$ are