Find the length of the chord intercepted by the
(a) circle x2 + y2 – 8x – 6y = 0 and the line x – 7y – 8 = 0
(b) circle x2 + y2 = 9 and the line x + 2y = 3
(c) circle x2 + y2 – 6x – 2y + 5 = 0 and the line x – y+ 1 = 0
(a) Given centre (4,3)
r= (\sqrt{16 + 9}) = √25 = 5
P = length of the perpendicular from (4, 3) to the line x – 7y – 8 = 0
Length of the chord = 2 . (\sqrt{r^2 - p^2})
L = 5√2 units
(b) Centre (0,0), r = 3, Line x + 2y – 3 = 0
