QJEEM12Ma67ab: JEE Main 2012 Mathematics - Class 11 JEEM12Ma67ab Solution: The length of the diameter of the circle which touches the x…

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

Let center of the circle be

(1, h)

[

as circle touches

x

-axis at

(1, 0)]

Let the circle passes through the point

B (2, 3)

∴

C A = C B

(radius)

\Rightarrow C A^{2} = C B^{2}

\Rightarrow {(1 - 1)}^{2} + (h - 0)^{2} = {(1 - 2)}^{2} + {(h - 3)}^{2}

\Rightarrow h^{2} = 1 + h^{2} + 9 - 6 h

\Rightarrow h = \frac{10}{6} = \frac{5}{3}

Thus, diameter is

2 h = \frac{10}{3} .

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