How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?

The equation of a circle is:

(x - h)² + (y - k)² =  radius²

where (h, k) is the center. 

We can plug in the given information from the description and solve for the radius.

(x - 2)² + (y - 4)² = radius²

To find the radius, we do the distance formula from the center to the point on the circle. 

Distance = 

D = 
D = 
D = 
D = 

That is your radius. Now we plug it in.

(x - 2)² + (y - 4)² = (√34)²

Your final answer is:

(x - 2)² + (y - 4)² = 34