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

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Statement 1 is true, statement 2 is true and statement 2 is a correct explanation for statement1

Statement 1 is false, statement 2 is true

Statement 1 is true, statement 2 is false

Statement 1 is true, statement 2 is true but statement 2 is not a correct explanation for statement 1

answer is A.

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Detailed Solution

$x^{2} + y^{2} - 6 x + 2 y = 0 centre = (3, - 1), r = \sqrt{10} (3, - 1) lies on 2 x + y = 5 s t a t e m e n t - 1 i s n o t t r u e a s t h e r e a r e i n f i n i t e c i r c l e s a c c o r d i n g t o t h e g i v e n c o n d i t i o n s . (3, - 1) is also lies on 2 x + y = 5 and it is a normal statement - 2 is true$