The locus of mid-points of the line segments joining ($$-$$3, $$-$$5) and the points on the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$$ is :

An angle of intersection of the curves, $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and x² + y² = ab, a > b, is :

The line $$12x\cos \theta + 5y\sin \theta = 60$$ is tangent to which of the following curves?

If x² + 9y² $$-$$ 4x + 3 = 0, x, y $$\in$$ R, then x and y respectively lie in the intervals :