SOLUTION: solve and graph {{{ 25x^2-16y^2-100x-96y-444=0 }}}

Question 578884: solve and graph
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
solve and graph
25x^2-16y^2-100x-96y-444=0
complete the square
25(x^2-4x+4)-16(y^2+6y+9)=444+100-144=400
25(x-2)^2-16(y+3)^2=400
divide by 400=
(x-2)^2/16-(y+3)^2/25=1
This equation is that of a hyperbola with horizontal transverse axis of the standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.
..
For given equation:
center: (2,-3)
a^2=16
a=4
vertices: (2�a,-3)=(2�4,-3)=(-2,-3) and (6,-3)
..
b^2=25
b=5
length of conjugate axis=2b=10
..
slope of asymptotes=�b/a=�5/4
Asymptotes are straight lines which go thru the center
Equations for asymptotes:
y=(5/4)x+b
solving for b
-3=(5/4)*2+b
b=-11/2=-5.5
equation:
y=5x/4-5.5
..
y=(-5/4)x+b
solving for b
-3=(-5/4)*2+b
b=-.5
equation:
y=-5x/4-.5
..
See graph below:
y=�(25(x-2)^2/16-25)^.5-3

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