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Question

The equation of a circle which contains the points A(2,-2)
B(-1,-3) and C(0,-1) is x^2+y^2+__x+__y+4=0

Answer 1

you just have to plug in the numbers... make those empty spaces your variables a and b

(2)^2+(-2)^2+a(2)+b(-2)+4=0 ------ once simplified you get
12=-2a+2b

(-1)^2+(-3)^2+a(-1)+b(-3)+4=0 ------once this one is simplified you get
14=a+3b
make a change and it looks like this a=14-3b
and now you make a substitution
so 12=-2(14-3b)+2b
b=5 and a=-1

Answer 2

One easy way would be to plug in the points and see what values you need to make the equation true for all three points.

Let's use P and Q to represent the unknown values:
x² + y² + Px + Qy + 4 = 0

Plug-in the values for point A (2, -2):
2² + (-2)² + P(2) + Q(-2) + 4 = 0
4 + 4 + 2P - 2Q + 4 = 0
2P - 2Q = -12
P - Q = -6

Do the same for point B (-1, -3)
(-1)² + (-3)² + P(-1) + Q(-3) + 4 = 0
1 + 9 - P - 3Q + 4 = 0
P + 3Q = 14

And again for point C (0, -1)
(0)² + (-1)² + P(0) + Q(-1) + 4 = 0
1 - Q + 4 = 0
Q = 5

From here we can go back and figure out P:
P - Q = -6
P - 5 = -6
P = -1

So the final equation that will include all 3 points is:
x² + y² - x + 5y + 4 = 0

Answer 3

x^2+y^2+(-1)x+(5)y+4=0

Answer 4

x^2+y^2+mx+ny+4=0

plug in 2 of A, B and C
A(2,-2)
4 + 4 + 2m -2n +4 = 0
n = m+6

C(0,-1)
0 + 1 + 0 -n + 4 = 0
n = 5
m = n-6 = -1

answer =
x^2 + y^2 -x +5y +4 = 0

Answer 5

center of circle = (0.5, - 2.5)
radius = 1.5811
equation
(x-.5)^2 + (y+2.5)^2 = 1.5811^2

x^2 - x + 1/4 + y^2 + 5 y + 25/4 = 2.5
x^2 + y^2 - x + 5y = 10/4 - 25/4 = - 15/4
x^2 + y^2 - x + 5y + 15/4

Answer 6

Standard circle equation (x+a)^2 + (y - b)^2 =r^2

Where (a, b) is center and r is radius!
if you look at points (-1,-3) and (2,-2) and find the mid point!

(.5, -2.5) now all your points are .5 off in one direction and 1.5 off in the other! (Each point is equidistant to it!)
length of the radius needs to be at that length!
.5^2 + 1.5^2 = ?
.25 + 2.25 = 2.5
so radius of 2.5 places every point on the circle! (back to formula!)
r^2 is standards form so 2.5^2 = 6.25
(x+.5)^2 + (y - 2.5)^2 =6.25

If you want all points inside of the circle choose anynumber larger than 6.25!

Answer 7

7 squared

Answer 8

I'd say one and a half years ago I could have done that, but my brain is dead from trying to remember how to spell certain words... It's been a while...

Answer 9

It doesn't exist.

Answer 10

okay, does ^ supposed to mean multiply?