Question

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

Answer 1

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

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