If the equation of a curve C is transformed to 9 x 2 + 25 y 2 = 225 by the rotation of the coordinate axes about the origin through an angle π 4 in the positive direction then the equation of the curve C , before the transformation is

Step-by-step solution

The original and new coordinates are, x = x cos π 4 - y sin π 4 = x 2 - y 2 y = x sin π 4 + y cos π 4 = x 2 + y 2 The equation of the curve is, 9 x 2 + 25 y 2 = 225 ⇒ x - y 2 2 + 25 x + y 2 2 = 225 After simplification, 9 x 2 + 9 y 2 + 18 x y + 25 x 2 + 25 y 2 - 50 x y = 450 ⇒ 34 x 2 + 34 y 2 - 32 x y = 450 ⇒ 17 x 2 + 17 y 2 - 16 x y = 225