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

Let $$P$$ be a variable point on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ with foci $${F_1}$$ and $${F_2}$$. If $$A$$ is the area of the triangle $$P{F_1}{F_2}$$ then the maximum value of $$A$$ is ..........

Let $$C$$ be the curve $${y^3} - 3xy + 2 = 0$$. If $$H$$ is the set of points on the curve $$C$$ where the tangent is horizontal and $$V$$ is the set of the point on the curve $$C$$ where the tangent is vertical then $$H=$$.............. and $$V=$$ .................

If we consider only the principle values of the inverse trigonometric functions then the value of
$$\tan \left( {{{\cos }^{ - 1}}{1 \over {5\sqrt 2 }} - {{\sin }^{ - 1}}{4 \over {\sqrt {17} }}} \right)$$ is