SOLUTION: Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± five divided by four times x..

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Question 1136097: Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± five divided by four times x..
Answer by MathLover1(20850) About Me  (Show Source):
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Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± (5/4)x.
The equation of this hyperbola in standard form:
y%5E2+%2F+a%5E2+-+x%5E2+%2F+b%5E2+=+1
y+= ±%28+a%2Fb+%29x
±%285%2F4%29x+= ±%28+a%2Fb+%29x
a+%2F+b+=+5+%2F+4
a+=+10
10+%2F+b+=+5+%2F+4
b+=+%2810%2A4%29%2F5
b+=+8

The equation of the hyperbola is:
y%5E2+%2F+10%5E2+-+x%5E2%2F+8%5E2+=+1
y%5E2+%2F+100+-+x%5E2%2F+64+=+1