SOLUTION: Find: a) (h,k) and radius r b) Graph the circle c) Find intercepts, if any (x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)

Algebra ->  Graphs -> SOLUTION: Find: a) (h,k) and radius r b) Graph the circle c) Find intercepts, if any (x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)       Log On


   

Question 1026883: Find:
a) (h,k) and radius r
b) Graph the circle
c) Find intercepts, if any
(x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find:
a) (h,k) and radius r
b) Graph the circle

(x^2)+(y^2)+x+y-(1/2)=0 or (x^2)+x+(y^2)+y=(1/2)
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x^2+x+y^2+y=1/2
Complete the squares for x and y
x^2+x+1/4 + y^2+y+1/4 = 1/2+1/4+1/4 = 1
(x+1/2)^2 + (y+1/2)^2 = 1
(h,k) = (-1/2,-1/2)
r = 1
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c) Find intercepts, if any
x^2+x+y^2+y=1/2
y = 0 --> x^2 + x - 1/2 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-0.5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A-0.5=3.

Discriminant d=3 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+3+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+3+%29%29%2F2%5C1+=+0.366025403784439
x%5B2%5D+=+%28-%281%29-sqrt%28+3+%29%29%2F2%5C1+=+-1.36602540378444

Quadratic expression 1x%5E2%2B1x%2B-0.5 can be factored:
1x%5E2%2B1x%2B-0.5+=+%28x-0.366025403784439%29%2A%28x--1.36602540378444%29
Again, the answer is: 0.366025403784439, -1.36602540378444. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-0.5+%29

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Intercepts are (x1,0) and (x2,0)
By symmetry, the y-ints are (0,x1) and (0,x2)