Question

If the endpoints of the diameter of a circle are (10, 12) and (0, 2), what is the standard form equation of the circle? A) (x + 5)2 + (y + 7)2 = 50 B) (x + 5)2 + (y + 7)2 = 5 2 C) (x − 5)2 + (y − 7)2 = 50 D) (x − 5)2 + (y − 7)2 = 5 2

Answer 1

So the equation of a circle is (x - h)² + (y - k)² = r² where (h,k) are the coordinates of the center of the circle and r is the radius. The diameter of a circle is a line that goes from one point of the circle to the other through the center of the circle. Well the center would be midway through the diameter so use midpoint formula to find the center which is (h,k) Mid point formula is both given x's added together divided by 2 for h and both y coordinates added together divided by 2 to find k
(10+0)/2
10/2= 5
(12+2)/2
14/2 = 7
so the center of the circle is (5,7) now use distance formula using the center and one of the points to the radius
√((5-10)²+(7-12)²)
√(-5²+ -5²)
√(25 + 25)
√50 is the radius
Now plug all found information into circle equation
(x-5)² + (y-7)² =50      note the end is 50 because the circle equation is radius squared and since the radius is √50, radius² is 50.
Answer is c

Answer 2

Answer:

its b

Step-by-step explanation:

(x + 10)2 + (y − 1)2 = 5

Substitute the endpoints (−8, 0) and (−12, 2) into the midpoint formula to find the center of the circle:

h =

−8 + (−12)

2

= −10

k =

0 + 2

2

= 1

Center: (−10, 1)

Use the distance formula to find the length of the radius. Remember that the radius is

1

2

the length of the diameter:

r =

1

2

(−8 − (−12))2 + (0 − 2)2

r =

1

2

(2

5

)

r =

5

Substitute values into standard equation of circle:

(x − h)2 + (y − k)2 = r2

(x − (−10))2 + (y − 1)2 = (

5

)2

(x + 10)2 + (y − 1)2 = 5