The points of intersection of the perpendicular tangents drawn to the ellipse 4 x 2 + 9 y 2 = 36 lie on the curve

Step-by-step solution

Given: 4 x 2 + 9 y 2 = 36 ⇒ x 2 9 + y 2 4 = 1 Comparing with the standard form x 2 a 2 + y 2 b 2 = 1 , we get a 2 = 9   &   b 2 = 4 Now, we know that the locus of two perpendicular tangents drawn to the ellipse is the director circle of the ellipse. Now, equation of the director circle to the ellipse x 2 a 2 + y 2 b 2 = 1 is given by x 2 + y 2 = a 2 + b 2 . Therefore, required curve is x 2 + y 2 = 9 + 4 or x 2 + y 2 = 13 .