Question

The equation of the circle passing through the point of intersection of the circles x² + y² – 4x – 2y = 8 and x² + y² – 2x – 4y = 8 and the point (–1,4) is

(a)  x² + y² + 4x + 4y – 8 = 0

(b)  x² + y² – 3x + 4y + 8 = 0

(c)  x² + y² + x + y – 8 = 0

(d)   x² + y² – 3x – 3y – 8 = 0

Answer 1

Correct option (d)   x² + y² – 3x – 3y – 8 = 0

Explanation:

Equation of any circle passing through the point of intersection of the circles is x² + y² – 4x – 2y – 8 + λ(x² + y² – 2x – 4y – 8) = 0 This circle passes through the point (–1,4)

1 + 16 + 4 – 8 – 8 + λ(1 + 16 + 2 – 16 – 8) = 0

5 – 5λ = 0 

λ = 1

Required circle is x² + y² – 3x – 3y – 8 = 0