The circles $${x^2} + {y^2} - 10x + 16 = 0$$ and $${x^2} + {y^2} = {r^2}$$ intersect each other in two distinct points if

The equation $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$ represents

The curve $$y = a{x^3} + b{x^2} + cx + 5$$, touches the $$x$$-axis at $$P(-2, 0)$$ and cuts the $$y$$ axis at a point $$Q$$, where its gradient is $$3$$. Find $$a, b, c$$.

Which one of the following curves cut the parabola $${y^2} = 4ax$$ at right angles?