(a) Write a pair of negative integers whose difference gives 8
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Answer:
Step-by-step explanation:
<u>General Equation Of A Circle </u>
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
