SOLUTION: x2 - 10x + y2 + 4y + 13 = 0 a. Find the corresponding standard form b. Identify the center and radius of the circle c. Find the x- and y-intercepts d. Graph the circle

Algebra ->  Rational-functions -> SOLUTION: x2 - 10x + y2 + 4y + 13 = 0 a. Find the corresponding standard form b. Identify the center and radius of the circle c. Find the x- and y-intercepts d. Graph the circle      Log On


   

Question 1062324: x2 - 10x + y2 + 4y + 13 = 0
a. Find the corresponding standard form
b. Identify the center and radius of the circle
c. Find the x- and y-intercepts
d. Graph the circle
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x2 - 10x + y2 + 4y + 13 = 0
Use ^ (Shift 6) for exponents.
x^2 - 10x + y^2 + 4y = -13
a. Find the corresponding standard form
complete the square for x, and for y.
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b. Identify the center and radius of the circle
(x-h)^2 + (j-k)^2 = r^2
Center at (h,k), radius = r
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c. Find the x- and y-intercepts
x-ints at y = 0, y-ints @ x = 0 (if any)
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d. Graph the circle

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a. x%5E2+-+10x+%2B+y%5E2+%2B+4y+%2B+13+=+0
x%5E2+-+10x+%2B+y%5E2+%2B+4y+=+-13
Completing squares:

%28x%5E2+-+10x+%2B+25%29+%2B+%28y%5E2+%2B+4y+%2B4%29+=+16
highlight%28%28x-5%29%5E2+%2B+%28y%2B2%29%5E2+=+16%29 or highlight%28%28x-5%29%5E2+%2B+%28y%2B2%29%5E2+=+4%5E2%29

b. The radius is highlight%284%29 ,
the number squared on the right side of the equation above.
The coordinates of the center are the solution for the shrunken circle with radius=0 ,
%28x-5%29%5E2+%2B+%28y%2B2%29%5E2+=+0 --> system%28x-5=0%2Cy%2B2=0%29 --> highlight%28system%28x=5%2Cy=-2%29%29

c. The x-intercepts:
The x-intercepts are the points (if any) where y=0 ,
where the graph of the equation crosses the x-axis.
To find them, we solve
system%28y=0%2Cx%5E2+-+10x+%2B+y%5E2+%2B+4y+%2B+13+=+0%29-->system%28y=0%2Cx%5E2+-+10x+%2B+13+=+0%29-->%22...%22-->highlight%28system%28y=0%2Cx=5+%2B-+2sqrt%283%29%29%29 ,
or we solve
system%28y=0%2C%28x-5%29%5E2+%2B+%28y%2B2%29%5E2=16%29-->system%28y=0%2C%28x-5%29%5E2%2B2%5E2=16%29-->system%28y=0%2C%28x-5%29%5E2%2B4=16%29-->system%28y=0%2C%28x-5%29%5E2=16-4%29-->system%28y=0%2C%28x-5%29%5E2=12%29-->system%28y=0%2Cx=5+%2B-+sqrt%2812%29%29-->highlight%28system%28y=0%2Cx=5+%2B-+2sqrt%283%29%29%29 .
Theapprocimate values for the y=coordinates of those points are
highlight%28y=about1.536%29 and highlight%28y=about8.464%29 .

The y-intercepts:
The y-intercepts are the points (if any) where x=0 ,
where the graph of the equation crosses the x-axis.
To find them, we solve
system%28x=0%2Cx%5E2+-+10x+%2B+y%5E2+%2B+4y+%2B+13+=+0%29-->system%28x=0%2Cy%5E2+%2B+4y+%2B+13+=+0%29-->%22...%22--> no solution ,
or we solve
system%28x=0%2C%28x-5%29%5E2+%2B+%28y%2B2%29%5E2+=+16%29-->system%28x=0%2C25%2B%28y%2B2%29%5E2=16%29-->system%28x=0%2C%28y%2B2%29%5E2=16-25%29-->system%28x=0%2C%28y%2B2%29%5E2=-9%29--> no solution >
The graph does not cross the y-axis.
In fact, it looks like this: