# What is the standard form of the equation of a circle with center (0,4) and radius 3/2?

Mar 28, 2018

Equation of circle is ${x}^{2} + {y}^{2} - 8 y + 13.75 = 0$

#### Explanation:

The center-radius form of the circle equation is

(x – h)^2 + (y – k)^2 = r^2, with the center being at the point

$\left(h , k\right)$ and the radius being r ; h=0,k=4,r=3/2=1.5.

Equation of circle is (x – 0)^2 + (y – 4)^2 = 1.5^2 or

x ^2 + y^2 – 8y+16 - 2.25=0 or x^2+y^2-8y+13.75=0.

Equation of circle is ${x}^{2} + {y}^{2} - 8 y + 13.75 = 0$

graph{x^2+y^2-8y+13.75=0 [-20, 20, -10, 10]} [Ans]