Assertion :Statement-1: The centre of the circle passing through the points $(3, 8)$ and $(5, 4)$ and having smallest radius is $(4, 6)$ . Reason: Statement-2: The centre of circle passing through two given points lies at mid-point of the line joining the points.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
The radius of the circle is smallest when the line joining the given points is a diameter of the circle
and thus the centre lies at the mid point of the line joining $(3, 8)$ and $(5, 4)$ i.e. $(4, 6)$ . so
Statement- $1$ is true but Statement- $2$ is false as the line joining the given points may not be a diameter for each circle passing through these points.

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Choose the correct option.

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Assertion :Statement-1: The centre of the circle passing through the points (3,8) and (5,4) and having smallest radius is (4,6). Reason: Statement-2: The centre of circle passing through two given points lies at mid-point of the line joining the points.

Assertion :Statement-1: The centre of the circle passing through the points $(3, 8)$ and $(5, 4)$ and having smallest radius is $(4, 6)$ . Reason: Statement-2: The centre of circle passing through two given points lies at mid-point of the line joining the points.