Question

Show that the line 4x – y = 17 passes through the centre of the circle x² + y² – 8x + 2y = 0.

Answer 1

Given x² + y² – 8x + 2y = 0 & line 4x – y = 17 c = (4, -1) 

C must lie on the line 4x – y = 17 

4(4) - (-1) = 17 

16 + 1 = 17 ⇒ 17 = 17 

Hence the line 6x – y = 17 passes through the centre.