Will give brainliest!

write the general equation for the circle that passes through the points: (1, 7) (8, 6) (7, -1)

Step-by-step explanation:

General Equation Of A Circle

If a,b, and c are real numbers, then the general equation of a circle is

There are three unknowns that could eventually be determined if we knew three points of the circle. These points are (1, 7) (8, 6) (7, -1). We only need to replace them in the general equation and solve the resulting system of equations

For the point (1, 7)

Operating and rearranging

For the point (8, 6)

Operating and rearranging

For the point (7, -1)

Operating and rearranging

We form the system of equations

We'll eliminate c from the first two equations and then from the last two equations

Multiplying the first one by -1

Adding them up we have

Adding up with the third equation

We get

c=0

Knowing this value, let's return to the original system with c=0

Multiplying the first by -8

Adding them up

Which gives  

Finally, isolating a from

We get

a=-8

So the general equation of the circle is

the 3rd option is right

step-by-step explanation: