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 .

Question

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 .

TestHub · Accepted Answer

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.

Mathematics - Circle Question with Solution | TestHub

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