Question

The radius of the circle represented by the equation 3x² + 3y² + λxy + 9x + (λ − 6) y + 3 = 0 is

Options

• \[\frac{3}{2}\]

• \[\frac{\sqrt{17}}{2}\]

•  2/3

• none of these

Answer 1

\[\frac{3}{2}\]

The equation of the circle is 3x² + 3y² + λxy + 9x + (λ − 6) y + 3 = 0.
∴ Coefficient of xy = 0

\[\Rightarrow \lambda = 0\]

\[\therefore 3 x^2 + 3 y^2 + 9x - 6y + 3 = 0\]

\[ \Rightarrow x^2 + y^2 + 3x - 2y + 1 = 0\]

Therefore, the radius of the circle is

\[\sqrt{\left( \frac{3}{2} \right)^2 + \left( - 1 \right)^2 - 1} = \frac{3}{2}\] .