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C2 Coordinate geometry

The circle C has equation x2 + y2 − 8x − 16y + 72 = 0.

a) Find the coordinates of the centre and the radius of C.

b) Find the distance of the centre of C from the origin in the form kroot5.
The point A lies on C and the tangent to C at A passes through the origin O.

c) Show that OA = 6root2.

Can sum1 help plz!

Reply 1

Dekota

Fenchurch

The circle C has equation x2 + y2 − 8x − 16y + 72 = 0.
a) Find the coordinates of the centre and the radius of C.

x^2 + y^2 − 8x − 16y + 72 = 0

a) x^2 - 8x + y^2 − 16y + 72 = 0
=> (x-4)^2 - 16 + (y−8)^2 - 64 + 72 = 0
=> (x-4)^2 + (y−8)^2 = 8

centre = (4, 8)
radius = sqrt(8)

b) Find the distance of the centre of C from the origin in the form kroot5.