What is the equation for a circle?

Question

What is the equation for a circle in the coordinate plane whose center is at (-2, 5) and goes through the
point (1, 5)?

Answer 1

An equation of the circle is (x-h)²+(y-k)² = r², where the center is (h,k) and r is the radius.  

 

So, we know that h = -2 and k = 5.  

 

The radius is the distance from the center to any point on the circle.  

 

So, r = √[(-2-1)²+(5-5)²] = 3

 

Therefore, the equation is (x+2)²+(y-5)² = 9

 

 

Answer 2

The equation for a circle is (x - h)² + (y - k)² = r²   where the ordered (h,k) is the center and r is the radius.

 

we have the center (-2,5) and need the radius.

 

plot the center and given point on the circle to find the radius.  You should see the radius = 3.

 

now plug values into equation

 

(x - h)² + (y - k)² = r²

 

(x - (-2))² + (y - 5)² = 3²

 

(x  + 4)² + (y - 5)² = 9