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 $\frac{10}{3}$

Since the circle touches x-axis at the point (1,0),

The center must be of form (1,k).

Now,

Distance between (1,k) and (1,0) = Distance between (1,k) and (2,3) = r

$\to k=\sqrt{(1-2{)}^2+(k-3{)}^2}$

$\to k^2=1+k^2+9-6k$

$\to k=\frac{5}{3}$

Thus, diameter,

$=r\times 2$

$=$ Distance between (1,0) and (1,k) $\times 2$

$=k\times 2$

$=\frac{10}{3}$

Hence, (A) is the correct answer.