Question

Equation of circle through intersection of x² + y² + 2x = 0 and x – y = 0, having minimum radius is-

• A. x² + y² – 1 = 0
• B. x² + y² – x – y = 0
• C. x² + y² – 2x – 2y = 0
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Equation of required circle is

x² + y² + 2x + l (x – y) = 0

whose centre of circle is $\left( \frac{2 + \lambda}{2}, - \frac{\lambda}{2} \right)$

and radius of circle

= $\sqrt{\left( \frac{2 + \lambda}{2} \right)^{2} + \frac{\lambda^{2}}{4}} = \sqrt{\frac{(\lambda + 1)^{2} + 1}{2}}$ .

Radius of circle is minimum when l = – 1.

Hence, required equation of circle is x² + y² + x + y = 0