Q.
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 $x^{2}+y^{2}-6x+2y=0.$
Solution:
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.
