Question

The length of the diameter of the circle which touches the x-axis at the point $(1,0)$ and passes through the point $(2,3)$ is:

• A. $\frac{10}{3}$
• B. $\frac{3}{5}$
• C. $\frac{6}{5}$
• D. $\frac{5}{3}$

Answer 1

The correct option is A $\frac{10}{3}$

Let $(h,k)$ be the centre .

$(h-1{)}^2+(k-0{)}^2=k^2\Rightarrow h=1$

$(h-2{)}^2+(k-3{)}^2=k^2\Rightarrow k=\frac{5}{3}$

$\therefore$ diameter is $2k=\frac{10}{3}$

Hence, option 'A' is correct.