Question

When the axes are rotated through an angle π/6, find the transformed equation of x² + 2√3 xy - y² =2a².

Answer 1

Since θ = π/6 , x = X cos α – Y sin α

x = X cos π/6 – Y sin π/6

= X. √3/2 − Y.1/2 = (√3X - Y)/2

y = X sin α + Y cos α = X. sin (π/6) + Y cos (π/6)

= X. (1/2) + Y.√3/2 = (X + √3Y)/2

Transformed equation is f

⇒ 8X² – 8Y² = 8a² ⇒ X² – Y² = a²