How do you write an equation for a circle given center (0,3) and radius is 7 units?

1 Answer
Jan 10, 2017

Answer:

# x^2 + (y-3)^2 = 7^2 #, or
# x^2 + y^2-6y-40 =0 #

Explanation:

The Cartesian equation of a circle with centre #(a,b)# and radius #r# is:

# (x-a)^2 + (y-b)^2 = r^2 #

So a circle with centre #(0,3)# and radius #7# would be:

# (x-0)^2 + (y-3)^2 = 7^2 #
# :. \ \ \ \ \x^2 + (y-3)^2 = 7^2 #

We can multiply out if required to get:

# \ \ \ \ \ \ \x^2 + y^2-6y+9 = 49 #
# :. x^2 + y^2-6y-40 =0 #