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Statement I: The only circle of radius sqrt(10) having a diameter lying along the line 2x + y = 5 is x² + y² - 6x + 2y = 0. Statement II: The line 2x + y = 5 is a normal to the circle x² + y² - 6x + 2y = 0. Choose the correct option.

1. Statement I is false, Statement II is true
2. Statement I is true; Statement II is false.
3. Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement I.
4. Statement I is true; Statement II is true; Statement II is a correct explanation of Statement I.

Correct answer: Statement I is false, Statement II is true

Solution

Centre (3,-1) lies on 2x+y=5 and radius = sqrt(10), so Statement II (line is a normal, i.e. passes through centre) is true; but infinitely many circles of radius sqrt(10) can have a diameter along that line, so Statement I (uniqueness) is false.

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