Problem in Polar coordinates
1. The curve C has polar equation
r^2 cos 2Ѳ = a^2, -pi/4 < Ѳ < pi/4
Find in terms of the positive constant a
(a) the area of the region bounded by the half-lines Ѳ = + pi/6 and the arc of the curve C in the interval -pi/6 < Ѳ < pi/6
(b) the equation of the tangent to the curve which is perpendicular to the initial line, giving your answer in polar form.
2. The curve C has polar equation r = a sin Ѳ sin 2Ѳ, where a is a positive constant and 0 ≤ Ѳ ≤ pi/2.
(a) Find, in terms of a, the area of the region enclosed by C.
(b) Show that the tangent at the point (3/4a, pi/3) is parallel to the initial line.
Please help me to solve these questions. Please help me.