Question

The centre of the circle touching the y-axis at $(0,3)$ and making an intercept of $2$ units on the positive x-axis is

• A. $(10,\sqrt{3})$
• B. $(\sqrt{3},10)$
• C. $(\sqrt{10},3)$
• D. $(3,\sqrt{10})$

Answer 1

Answer: (C)

$(\sqrt{10},3)$

$|x_2-x_1|=2$

$e{q}^n$ of circle is

$(x-h{)}^2+(y-3{)}^2=h^2$

x-intercept : $(x-h{)}^2+g=h^2$

$x^2-2hx+g=0$

$|x_1-x_2|=\sqrt{4h^2-36}$

$2=\sqrt{4h^2-36}$

$4h^2=40$

$h^2=10$

$h=\sqrt{10}$

Centre$\equiv (\sqrt{10},3)$