Statement 1: The only circle having radius 10 and a diameter along line 2x + y = 5 is x^2 + y^2 - 6x + 2y = 0. Statement 2 : 2x + y = 5 is a normal to the circle x^2 + y^2 - 6x + 2y = 0.

JEE Main 2013 Mathematics question

Statement 1: The only circle having radius and a diameter along line 2x + y = 5 is . Statement 2 : 2x + y = 5 is a normal to the circle .

(1)Statement 1 is false; Statement 2 is true.Correct
(2)Statement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(3)Statement 1 is true; Statement 2 is false.
(4)Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

Answer: (1)

The given circle has centre (3, −1) and radius , and 2(3) + (−1) = 5, so the line passes through the centre — a normal (Statement 2 true).

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Question ID VK-104234