Question

find the centre and radius of the circle x2+y2-4X-8Y-45=0

Answer 1

comparing the eq. x2+y2-4x-8y-45=0 with the standard eq. of circle

i.e., x2+y2+2gx+2fy+c=0

then, 2g = -4, g = - 2

and, 2f = -8 , f = -4

and, c = -45

as, the centre of circle is (-g,-f)

centre = (2,4)

and, radius(square) = g2+f2-c

hence, radius = (root)65

Answer 2

Answer:

comparing the eq. x2+y2-4x-8y-45=0 with the standard eq. of circle

i.e., x2+y2+2gx+2fy+c=0

then, 2g = -4, g = - 2

and, 2f = -8 , f = -4

and, c = -45

as, the centre of circle is (-g,-f)

centre = (2,4)

and, radius(square) = g2+f2-c

hence, radius = (root)65

Explanation: