Given that the equation of the circle is x^2 + y^2 +2x -8y+5 =0

Question

(i)Find the centre and radius of the circle
(ii)Determine whether the line x-3y=8 is tangent to the given circle

Answer 1

1. x^2+2x+(2/2)^2+Y^2-8y+(-8/2)^2=-5+1+16.
X^2+2x+1 + Y^2-8y+16 = 12.
(x+1)^2 + (y-4)^2 = 12.
(x-h)^2 + (y-k)^2 = r^2.

C(h,k).
C(-1,4).

r^2 = 12.
r = 2*sqrt3 = 3.46.