The transformed equation of 3 x^2+3 y^2+2 x y=2 , when the coordinate axes are rotated through an angle of 45^ , is

Step-by-step solution

Since, the axes are rotated through an angle 45^ , then we replace (x, y) by (x 45^ -y 45^ , x 45^ +y 45^ ) ie, ( x 2 - y 2 , x 2 + y 2 ) in the given equation 3 x^2+3 y^2+2 x y=2 array rrr 3 ( x 2 - y 2 )^2+3 ( x+y 2 )^2 & +2 ( x-y 2 ) ( x+y 2 )=2 & 3 2 (x^2+y^2+2 x y )+ 3 2 (x^2+y^2-2 x y ) & & + 2 2 (x^2-y^2 )=2 & 4 x^2+2 y^2=2 & 2 x^2+y^2=1 array