SOLUTION: identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci 5x^2-5y^2+4

Question 1010718: identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci
5x^2-5y^2+40x-20y+35=0
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

.........all terms divide by

...complete squares

=> both sides divide by
=> so, we have a hyperbola with ,
the center is at (,)
semimajor axis length |~~
semiminor axis length | ~~

foci is fixed distance from the center
=>=>

so, foci is at:
(,) and (,)~~(, ) and (, )
vertices | (,) and (, )~~(, ) and (, )

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

identify the conic section if it is a parabola give the vertex if it is a circle give the center and radius if it is a ellipse or a hyperbola give the center and foci
5x^2-5y^2+40x-20y+35=0

This is INDEED a HYPERBOLA, since higher-degree x and y have different signs.
However, that person is WRONG, as usual, because the equation you're looking for is:
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