SOLUTION: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. x2 − y2 = 8(x − y)

Question 959131: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution.
x2 − y2 = 8(x − y) + 1
If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the focus, vertex, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. (Enter your answers for asymptotes as a comma-separated list of equations. If an answer does not exist, enter DNE.)
Sketch the graph of the equation.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

....since we see that and =>=>=>

so, it is hyperbola
and we see that
semimajor axis length ,
semiminor axis length ,
=> then =>=> or
since ,, the center is at (,)
foci:
(,) | (, )
((, ) | (, ))
approximately:
(, ) | (,)
vertices:
since the center is at (, ) = (, ) and the vertices are units to either side, then vertices are at
(, ) | (, )
(, ) | (, )
asymptotes:
and

Sketch the graph of the equation.

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SOLUTION: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. x2 &#8722; y2 = 8(x &#8722; y)

SOLUTION: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, a degenerate conic, or results in no solution. x2 − y2 = 8(x − y)