Find the equation of the circle described. Write your answer in standard form. The coordinates of the center are (0, −4) and the length of the diameter is 6.

Question

Find the equation of the circle described. Write your answer in standard form.

The coordinates of the center are (0, −4)

 and the length of the diameter is 6.

Answer 1

The general equation of a circle:

(x + a)² + (y + b)² = r²

we are given r = 3, and b = +4. There is no x offset, so a = 0

So:

x² + (y + 4)² = 9

So why is b = +4 ??....A positive offset means that the variable must go negative for the term to go to zero.

Always make a sketch to verify that you have the right answer

Answer 2

The standard form of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center point of the circle, and r is the radius. Remember the radius is half the length of the diameter. So, if we plug in the center (0, -4) and the radius,3, (half of the diameter), then the equation would be:

(x-0)² + (y-(-4))² = (3)²

then simplify to get,

x²+(y+4)²=9