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

• Correct answer
  A

  Statement 1 is false; Statement 2 is true.
• B

  Statement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
• C

  Statement 1 is true; Statement 2 is false.
• D

  Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

Solution

Circle: $x^2+y^2-6 x+2 y=0$ Line: $2 x+y=5$ Centre $=(3,-1)$ Now, $2 \times 3-1=5$, hence centre lies on the given line. Therefore line passes through the centre. The given line is normal to the circle. Thus statement- 2 is true, but statement- 1 is not true as there are infinite circle according to the given conditions.

Hence, the correct answer is option: 'A'.