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 is  (d) x² +y² –3x–3y–8 = 0

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

5–5 λ = 0

λ = 1

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