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  4. 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 :

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Q. 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 :

AIEEEAIEEE 2012Conic Sections

Solution:

Now
$h^{2} = \left(1 - 2\right)^{2} + \left(h - 3\right)^{2}$
$0 = 1 - 6h + 9$
$6h = 10$
$h = \frac{5}{3}$
Now diameter is $2h = \frac{10}{3}$

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