The eccentric angle of the point P (-6,2) of the ellipse x^2 48 + y^2 16 =1 is

Step-by-step solution

The ellipse is defined by the equation x^2 48 + y^2 16 =1 . By comparing with the standard form x^2 a^2 + y^2 b^2 =1 , we find a=4 3 and b=4 . The parametric coordinates of any point on the ellipse are given by (a , b ) , where is the eccentric angle. For the point P (-6,2) , we set: 4 3 = -6 and 4 = 2 . Solving the second equation gives = 1 2 . From the first equation, = -6 4 3 = - 3 2 after rationalization. Given that is positive and is negative, must lie in the second quadrant. The reference angle where = 1 2 an