Hi,

Can you please work out the solutions for these questions I'm in need of desperate help.

COMPONENT 3: Point A(A, A*) and Point B(B, B*) are points on the parabola y = x- , A > 0 The two tangents at point A and B are perpendicular, another parabola is also shown above for (part F) the shaded region bounded by y = x* and the tangents is for (part G). A) Show that the equation of the tangent to parabola y = x- at Point A(A, A ) is y = 2ax - a? ? B) Show that the equation of the tangent to parabola y = x at 1 Point B(B, B ) is perpendicular to y = 2ax - ax* is y = - X 2a 1602 C) Show that b = =? 4aD) Show that the above two tangents to parabola y = x* intersect at 40--1 Point Cl Ba 1 E) Find the length of AC and BC hence show that the area of AABC is (= + 4a) 256F) Does such a right angle exist for other parabola of the form y = kx= ? Verify your answer by two suitable values of ke R/(1) (all positive real numbers except 1) of your choice