Circe Equation??

Question

Circles are really hard for me to grasp.. how/what would be the equation with this information provided?

 

Write the equation of the circle centered at (-4 , 8 ) that passes through (-6,-20).

Answer 1

The standard form equation of a circle is (x-h)² + (y-k)² = r² where the point (h, k) is the center, and r is the radius. In this problem, you're given the center, so h=-4 and k = 8. You just need to find the radius.

 

By definition, the radius is the distance from the center of the circle to its edge. You know the point (-6,-20) is on the edge of the circle, so you can use that to find r².

 

The distance formula is d² = (x₂-x₁)² + (y₂-y₁)², so:

 

r² = (-6 - -4)² + (-20 - 8)²

 

Be careful with all the negatives, but you should be able to find the radius here, and can now substitute all the values you need into the standard equation.