Question

30 points and BRAINLIEST!

Answer 1

Answer:

(x − 4)² + (y − 3)² = 25

Step-by-step explanation:

The equation of a circle is:

(x − h)² + (y − k)² = r²

Given three points on the circle, we can write three equations:

(1 − h)² + (7 − k)² = r²

(8 − h)² + (6 − k)² = r²

(7 − h)² + (-1 − k)² = r²

Expanding:

1 − 2h + h² + 49 − 14k + k² = r²

64 − 16h + h² + 36 − 12k + k² = r²

49 − 14h + h² + 1 + 2k + k² = r²

Simplifying:

50 − 2h + h² − 14k + k² = r²

100 − 16h + h² − 12k + k² = r²

50 − 14h + h² + 2k + k² = r²

Subtracting the first equation from the second and third equations:

50 − 14h + 2k = 0

-12h + 16k = 0

Solving the system of equations, first reduce:

25 − 7h + k = 0

-3h + 4k = 0

Solve with substitution or elimination.  Using substitution, solve for k in the first equation and substitute into the second.

k = 7h − 25

-3h + 4(7h − 25) = 0

-3h + 28h − 100 = 0

25h = 100

h = 4

k = 7h −25

k = 7(4) − 25

k = 3

Now plug these into any of the original three equations to find r.

(1 − h)² + (7 − k)² = r²

(1 − 4)² + (7 − 3)² = r²

9 + 16 = r²

25 = r²

The equation of the circle is:

(x − 4)² + (y − 3)² = 25

Graph: desmos.com/calculator/ctoljeqhnp