Write the general equation for the circle that passes through the points:

(1, 7)

(8, 6)

(7, -1)

You must include the appropriate sign (+ or -) in your answer. Do not use spaces in your answer.

x 2 + y 2
a0 x
a1 y = 0

The answer to your question is     x² + y² - 8x - 6y = 0

Step-by-step explanation:

Data

P (1, 7)

Q (8, 6)

R (7, -1)

Use the general equation of the Circle

                            x² + y² + Dx + Ey + F = 0

Process

1.- Substitute each point in the general equation and simplify

For P                                  

                          (1)² + (7)² + D + 7E + F = 0

                            1 + 49 + D + 7E + F = 0

                                 50 + D + 7E + F = 0

                                       D + 7E + F = -50             Equation l

For Q

                           (8)² + (6)² + 8D + 6E + F = 0

                            64 + 36 + 8D + 6E + F = 0

                            100 + 8D + 6E + F = 0

                                    8D + 6E + F = -100         Equation ll

For R

                           (7)² + (-1)² + 7D - E + F = 0

                           49 + 1 + 7D - E + F = 0

                                50 + 7D - E + F = 0

                                         7D - E + F = -50       Equation lll

Solve the system of equations, I do not include the process but the solutions are

D = -8   E = -6   F = 0

-Substitution

                       x² + y² - 8x - 6y = 0

D

Explanation: