The eccentricity of an ellipse whose centre is at the origin is 1 2 . If one of its directrices is x = - 4 , then the equation of the normal to it at 1 , 3 2 is:

Step-by-step solution

Given, e = 1 2 and a e = 4       ⇒ a = 2 ,  Also, b 2 = a 2 1 - e 2 ⇒ b 2 = 3 Equation of ellipse is x 2 4 + y 2 3 = 1       We know that, equation of normal to the ellipse x 2 a 2 + y 2 b 2 = 1 at x 1 ,   y 1 is a 2 x x 1 - b 2 y y 1 = a 2 - b 2 So, equation of normal at 1 ,   3 2 is 4 x 1 - 3 y 3 / 2 = 4 - 3 ⇒ 4 x - 2 y = 1