The equation of the circle passing through the point of intersection o

1.	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» 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

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»

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

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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

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