JEE Main · 2012 · 29 Apr 2012 · Offline · Circle

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)

(A) $\frac{10}{3}$ ✓ Correct
(B) $\frac{3}{5}$
(C) $\frac{6}{5}$
(D) $\frac{5}{3}$

Answer: (A)

Solution

Because the circle touches the

x

-axis at

(1, 0)

, its centre sits directly above that point at

(1, k)

and its radius equals

k

. Requiring the centre to be the same distance from

(2, 3)

gives

(1 - 2)^{2} + (k - 3)^{2} = k^{2}

, that is

1 + k^{2} - 6 k + 9 = k^{2}

, so

10 - 6 k = 0

and

k = \frac{5}{3}

. The diameter is twice the radius,

2 k = \frac{10}{3}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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