Mathematics - Circle Question with Solution | TestHub

Let$\left(a, 2\right)$be the centre of the circle

Equation of the circle is

${\left(x-a\right)}^2+{\left(y-2\right)}^2=a^{\mathrm{2 }}$

Put$\left(-\mathrm{1,0}\right)$in the equation of circle${\left(-1-a\right)}^2+{\left(-2\right)}^2=a^2$

$1+2a+a^2+4=a^2$

$2a=-5$

$a=-\frac{5}{2}$

Equation of circle is

${\left(x+\frac{5}{2}\right)}^2+{\left(y-2\right)}^2=\frac{25}{4}$

x intercept$=2\sqrt{g^2-c}$

$=2\sqrt{\frac{25}{4}-4}$

$=2\sqrt{\frac{9}{4}}$

$=3$