SOLUTION: Find the asymptote of a hyperbola with equation 25x^2 - 16y^2 = 400

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Question 1082534: Find the asymptote of a hyperbola with equation 25x^2 - 16y^2 = 400
Answer by MathLover1(20850) About Me  (Show Source):
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Find the asymptote of a hyperbola with equation 25x%5E2+-+16y%5E2+=+400+
first have to convert this equation to "conics" form by completing the square:
25x%5E2+-+16y%5E2+=+400
25x%5E2%2F400+-+16y%5E2+%2F400=+400%2F400+
x%5E2%2F16+-+y%5E2+%2F25=+1
or
%28x-0%29%5E2%2F16-+%28y-0%29%5E2+%2F25=+1
so, h=0 and k=0
a=4, b=5
the asymptes are then given by the straight-line equations
y=mx
In this case
b=5
a=4
So the slopes are m=5%2F4 and -5%2F4, and the asymptes are:
y+=+%285x%29%2F4 and y+=+-%285x%29%2F4