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: - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

Since the circle touches the x -axis at (1, 0), its centre is (1, k) and its radius is ∣ k ∣ .The equation of the circle is (x - 1)^{2} + (y - k)^{2} = k^{2} .The circle passes through (2, 3) : (2 - 1)^{2} + (3 - k)^{2} = k^{2} 1 + 9 + k^{2} - 6 k = k^{2} 10 - 6 k = 0 ⟹ k = 10/6 = 5/3 .Radius is 5/3 .Diameter is 2 k = 10/3 .

Try it yourself before checking the explanation above.

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:

\frac{10}{3}

\frac{3}{5}

\frac{6}{5}

\frac{5}{3}

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