Question

What is the equation of a circle with radius 4 and center (0,8)?

Answer 1

The equation of circle with the center at (h,k) is:

$\large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }$

r stands for radius. Therefore r^2 = diameter or 2×radius.

The question has already given the information we need, which are:

• radius = 4
• the center at (0,8)

Since the center is (h,k) - therefore the center is at h = 0 and k = 8 making it (h,k) = (0,8).

Substitute the values in the equation:

$\large{ {(x - 0)}^{2} + {(y - 8)}^{2} = {4}^{2} }$

Simplify to the simplest form

$\large \boxed{ {x}^{2} + {(y - 8)}^{2} = 16} \: \: \: \: \huge{ \green{\checkmark}}$

Answer

• The equation of a circle is x^2+(y-8)^2 = 16