The transformed equation of x^2+6 x y+8 y^2=10 when the axes are rotated through an angle 4 is :

Step-by-step solution

The given equation is x^2+6 x y+8 y^2=10 (i) Since axes are rotated through an angle 4 . x=x₁ 4 -y₁ 4 = x₁-y₁ 2 and y=x₁ 4 +y₁ 4 = x₁+y₁ 2 On putting the value of x and y in Eq. (i) ( x₁-y₁ 2 )^2+6 ( x₁-y₁ 2 ) ( x₁+y₁ 2 )+8 ( x₁+y₁ 2 )^2=10 x₁^2+y₁^2-2 x₁ y₁ 2 + 6 x₁^2-6 y₁^2 2 + 8 (x₁^2+y₁^2+2 x₁ y₁ ) 2 =10 x₁^2+y₁^2-2 x₁ y₁+6 x₁^2-6 y₁^2+8 x₁^2+8 y₁^2+16 x₁ y₁=20 15 x₁^2+3 y₁^2+14 x₁ y₁=20 Required equation is 15 x^2+14 x y+3 y^2=20