Question

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

• 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

The Correct Option is 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.