If a circle passing through the point (- 1, 0) touches y -axis at...

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

Equation of the circle is

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

Put \left(- 1,0\right)$in the equation of circle${\left(- 1 - a\right)}^{2} + {\left(- 2\right)}^{2} = {a}^{2}$<br /><br />$1 + 2a + {a}^{2} + 4 = {a}^{2}$<br /><br />$2a = - 5$<br /><br />$a = - \dfrac{5}{2}$<br /><br />Equation of circle is<br /><br />${\left(x + \dfrac{5}{2}\right)}^{2} + {\left(y - 2\right)}^{2} = \dfrac{25}{4}$<br /><br />x intercept$= 2\sqrt{{g}^{2} - c}$<br /><br />$= 2\sqrt{\dfrac{25}{4} - 4}$<br /><br />$= 2\sqrt{\dfrac{9}{4}}$<br /><br />$= 3