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  4. 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:

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Q. 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:

Conic Sections

Solution:

Equation of circle $(x-0)(x-a)+(y-1)(y-b)=0$
it cuts $x$-axis put $y=0 \Rightarrow x^2-a x+b=0$