The ends of diameter of a circle are the points 1,7) and (9,1) determine the equation of the circle

Question

Please answer this because this is my assignment for tomorrow..  And also give me the solution and formula how you solve it. Thank you very much 

Answer 1

Find the midpoint which will be the center of the circle.

 

The midpoint formula is ((x₁ + x₂)/2 , (y₁ + y₂)/2 )

 

(1 + 9)/2 , (7 + 1)/2

(5,4) is the center

 

Now the standard form for the equation of the circle is :

 

(x-h)² + (y-k)² = r² where the center is (h,k) and r = radius

 

We still need the radius which is equal to the distance from either of the points to the center

 

The distance formula is  √((x₁ - x₂)² + (y₁ - y₂)²

so the radius is √(9-5)² + (1-4)²

this equals √25 = 5

 

now we plug in 5 for r

 

(x-5)² +(y-4)² = 25