Question

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

• A. $x^2+ax+b=0$
• B. $x^2-ax+b=0$
• C. $x^2+ax-b=0$
• D. $x^2-ax-b=0$

Answer 1

The correct option is B $x^2-ax+b=0$

The circle equation is given by $(x-0)(x-a)+(y-1)(y-b)=0$

$⟹x^2+y^2-y(b+1)–ax+b=0$

This equations cuts the x-axis at $y=0$

$x^2–ax+b=0$

$x$ is given by the above equation

The abscissa are roots of the above equation.