Question

Equation of the circle, whose diameter is the chord x + y = 1 of the circles x² + y² = 4, is –

• A. x² + y² – x – y + 3 = 0
• B. x² + y² + x + y – 3 = 0
• C. x² + y² – x – y – 3 = 0
• D. None of these

Answer 1

Answer: (C)

x² + y² – x – y – 3 = 0

Answer 2

S ŗ x² + y² – 4 = 0

L ŗ x + y – 1 = 0

Equation of required circle

S + lL = 0

x² + y² – 4 + l (x + y – 1) = 0

x² + y² + lx + ly – l – 4 = 0 . . . (1)

Centre $\left( - \frac{\lambda}{2}, - \frac{\lambda}{2} \right)$

Lies on x + y = 1

Ž $- \frac{\lambda}{2} - \frac{\lambda}{2}$= 1

Ž l = – 1

So equation is x² + y² – x – y – 3 = 0