If 2x2 + λxy + 2y2 + (λ – 4) x + 6y – 5 = 0 is the equation of a circle, then its radius is
Given that the equation of the circle is:
⇒ 2x2 + λxy + 2y2 + (λ - 4)x + 6y - 5 = 0 ..... (1)
Comparing with the standard equation of circle:
⇒ x2 + y2 + 2ax + 2by + c = 0
We get
⇒ λ = 0
Substituting λ value in (1), we get
⇒ 2x2 + 0xy + 2y2 + (0 - 4)x + 6y - 5 = 0
⇒ 2x2 + 2y2 - 4x + 6y - 5 = 0
⇒
We know that for a circle x2 + y2 + 2ax + 2by + c = 0
⇒ Centre = (- a, - b)
⇒ Radius =
⇒ Radius (r) =
⇒
⇒
⇒
∴The correct option is (d)