The edges of the diameter of a circle are at (-3,-8) and (5,7).
Write the equation of the circle in general form.
Please show your work.

  x^2 + y^2 -2x +y -71 = 0

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is ...

  ((-3, -8) +(5, 7))/2 = (-3+5, -8+7)/2 = (1, -1/2)

The square of the radius of the circle can be found from the Pythagorean theorem. The x- and y- differences between an end point and the center are the legs of a right triangle with r as the hypotenuse.

  r^2 = (5 -1)^2 +(7 -(-1/2))^2 = 4^2 +7.5^2 = 16 +56.25

  r^2 = 72.25

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The standard form equation of the circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

  (x -1)^2 +(y -(-1/2))^2 = 72.25

Eliminating parentheses, we have ...

  x^2 -2x +1 +y^2 +y +0.25 = 72.25

Subtracting the right-side constant and rearranging to descending powers, we find the general form of the equation to be ...

  x^2 + y^2 -2x +y -71 = 0

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Comment on the work

Of course, you know that ...

  (a -b)^2 = a^2 -2ab +b^2

This helps you simplify the squares of binomials.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.