The pair of lines represented by $$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$$

are perpendicular to each other for :

If the pair of lines

$$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$

intersect on the $$y$$-axis then :

Identify the pair whose dimensions are equal

A ball whose kinetic energy E, is projected at an angle of $$45^\circ $$ to the horizontal. The kinetic energy of the ball at the highest point of its height will be