Question

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

• 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

Answer 1

Answer: (A)

Circle: $x^2+y^2-6x+2y=0$ ...(i)
Line : $2\times +3-1=5$ ...(ii)
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, hut statement-1 is not true as there are infinite circle according to the given conditions.