SOLUTION: what is the answer of this hyperbole: x^2 -4x-2y+10=0

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Question 867613: what is the answer of this hyperbole: x^2 -4x-2y+10=0
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-4x-2y%2B10=0

What is the question about the equation ?
It is NOT a hyperbola. If you want as a hyperbola, maybe you forgot to include an exponent:

x%5E2-4x-2y%5E2%2B10=0; but to be sure of which type of conic section, either do an appropriate check-test, or convert to standard form through completion of the square.

You should find
x%5E2-4x%2B4-2y%5E2=-10%2B4
%28x-2%29%5E2-2y%5E2=-6
.
highlight%28%28y%5E2%29%2F3-%28%28x-2%29%5E2%29%2F6=1%29.
This would be a hyperbola with center (2,0), vertices (2, -sqrt(3)), and (2, sqrt(3)).


Actually the parabola as originally expressed in equation:
Just as simple, maybe more simple.
Same term for completing the square in x.
x%5E2-4x-2y=-10
x%5E2-4x%2B10=2y
x%5E2-4x%2B4%2B10-4=2y
%28x-2%29%5E2%2B6=2y
Symmetric property and mult b.sds by (1/2),
highlight%28y=%281%2F2%29%28x-2%29%5E2%2B6%29.