SOLUTION: Give the coordinates of the center, foci, vertices, and asymptotes of the hy- perbola with equation 9x2 - 4y2 - 90x - 32y = -305. Sketch the graph, and include these points and lin

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Question 1180941: Give the coordinates of the center, foci, vertices, and asymptotes of the hy- perbola with equation 9x2 - 4y2 - 90x - 32y = -305. Sketch the graph, and include these points and lines, along with the auxiliary rectangle.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Give the coordinates of the center, foci, vertices, and asymptotes of the hyperbola with equation
..... I'll first have to convert this equation to "conics" form by completing the square






...........both sides divide by



,
Center: (,)

Major (transverse) axis length:
Semimajor axis length:
Minor (conjugate) axis length:
Semiminor axis length:



Foci:
(,)=(,)≈(,)
(,)=(,)≈(,)
Vertices:
the coordinates of the vertices are
(, ) and (, )
(, ) and (, )
(,), (,)
A hyperbola with a horizontal transverse axis and center at (,) has one asymptote with equation
and the other with equation

First asymptote:



Second asymptote:







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