has a diameter with endpoints (3,1) and (-7,6)

Question

Find the standard equation of the circle

Answer 1

Hi Dane,

 

to find the standard equation, you need the center of the circle and the radius

 

Find the midpoint of the diameter using the points (3,1) and (-7,6) This is the center of the circle.

 

(3 + -7)/2 = -2

 

(1 + 6)/2 = 3.5

 

The midpoiint, which is the center, is (-2 , 3.5)

 

Now you need the radius of the circle. This is equal to the distance from the center (-2 , 3.5) to either of the endpoints

 

distance formula   d = √(x₁ - x_2)² + (y₁ - y₂)²

 

d = √(3 - - 2)² + (1 - 3.5)²

 

d = √(25 + 6.25) = √31.25 = 5.59

 

So the standard equation is

 

(x + 2)² + (y - 3.5)² = 31.25