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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

5x%5E2-5y%5E2%2B40x-20y%2B35=0.........all terms divide by 5
x%5E2%2B8x-y%5E2-4y%2B7=0
%28x%5E2%2B8x%29-%28y%5E2%2B4y%29%2B7=0...complete squares
%28x%5E2%2B8x%2Bb%5E2%29-b%5E2-%28y%5E2%2B4y%2Bb%5E2%29-b%5E2%2B7=0
%28x%5E2%2B8x%2B4%5E2%29-4%5E2-%28y%5E2%2B4y%2B2%5E2%29-2%5E2%2B7=0
%28x%2B4%29%5E2-16-%28y%2B2%29%5E2-4%2B7=0
%28x%2B4%29%5E2-%28y%2B2%29%5E2-20%2B7=0
%28x%2B4%29%5E2-%28y%2B2%29%5E2-13=0
%28x%2B4%29%5E2-%28y%2B2%29%5E2=13=> both sides divide by 13
%28x%2B4%29%5E2%2F13-%28y%2B2%29%5E2%2F13=1=> so, we have a hyperbola with h=-4,k=-2
the center is at (-4,-2)
semimajor axis length |a=+sqrt%285%29~~a=2.24
semiminor axis length | b=sqrt%285%29~~b=2.24

foci is fixed distance c from the center
c%5E2+=+b%5E2+%2B+a%5E2=>c%5E2+=+%28sqrt%285%29%29%5E2+%2B+%28sqrt%285%29%29%5E2=>c%5E2+=+5+%2B+5
c=sqrt%2810%29
so, foci is at:
(-4-sqrt%2810%29,+-2) and (-4%2Bsqrt%2810%29,+-2)~~(-7.2, -2) and (-0.8, -2)
vertices | (-4-sqrt%285%29,+-2) and (-4%2Bsqrt%285%29, -2)~~(-6.2, -2) and (-1.8, -2)





Answer by MathTherapy(10552) About Me  (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: