Question

Find the values of a and b if the equation (a - 1)x² + by² + (b - 8)xy + 4x + 4y - 1 = 0 represents a circle.

Answer 1

Equation of the circle is (a - 1)x² + by² + (b - 8)xy + 4x + 4y - 1 = 0 

Equation of the circle will not have (xy) term.

∴ Co-efficient of (xy) term is 0

⇒ b - 8 = 0

⇒ b = 8   ....(1)

Also, for any circle,

Co-efficient of x² = Co-efficient of y²

⇒ a - 1 = b 

⇒ a - 1 = 8

⇒ a = 9

∴ a = 9 and b = 8