Statement 1: The only circle having radius 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 .

Step-by-step solution

Circle: x^2+y^2-6 x+2 y=0 Line: 2 x+y=5 Centre =(3,-1) Now, 2 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.