The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis at points whose abscissae are roots of the equation

Q: The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis at points whose abscissae are roots of the equation

(A) x2 + ax + b = 0

(B) x2 – ax + b = 0

(C) x2 + ax – b = 0

(D) x2 – ax – b = 0

Ans: (B)

Sol: The equation of the circle described on the line joining (0, 1), (a, b) as diameter is

(x – 0) (x – a) + (y-1) (y-b) = 0

or  x2+y2-ax-y(1+b)+b = 0

This meets the x-axis at y = 0

Therefore the abscissae of the points where the circle meets the x-axis are roots of the equation  x2-ax+b = 0

Hence (B) is the correct answer.