SOLUTION: trace the conic: x^2-3xy+y^2+10x-10y+21=0

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Question 1113225: trace the conic:
x^2-3xy+y^2+10x-10y+21=0
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
trace the conic:
Trace it from what?
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x^2-3xy+y^2+10x-10y+21
There's no equal sign.
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I copied and pasted x^2-3xy+y^2+10x-10y+21
There was no equal sign.
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You don't trace it, you graph it.
DL the FREE graph software at www.padowan.dk
Use F6, enter x^2-3x*y+y^2+10x-10y+21 = 0
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Notice the x*y.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-3xy%2By%5E2%2B10x-10y%2B21=0
We solve for y:

y%5E2-3xy-10y%2Bx%5E2%2B10x%2B21=0

y%5E2%2B%28-3xy-10y%29%2B%28x%5E2%2B10x%2B21%29=0

y%5E2%2B%28-3x-10%29y%2B%28x%5E2%2B10x%2B21%29=0

a=1, b=(-3x-10), c=(x²+10x+21)

y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+



y+=+%283x%2B10+%2B-+sqrt%28+%28-3x-10%29%28-3x-10%29-4%28x%5E2%2B10x%2B21%29%29%29%2F2+

y+=+%283x%2B10+%2B-+sqrt%28+9x%5E2%2B60x%2B100-4x%5E2-40x-84%29%29%2F2+

y+=+%283x%2B10+%2B-+sqrt%28+5x%5E2%2B20x%2B16%29%29%2F2+

Make a table of values using that formula

 x |      y
-10|-1.1 and -18.9
 -7|  0  and -11 
 -4|  1  and  -3
 -3|  1  and   0
 -2|imaginary
 -1|  4  and   3
  0|  7  and   3
  3| 15  and   4
 11| 36  and   7

Plotting some of those and others gives the rotated
and shifted hyperbola:



Edwin