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fiasKO [112]
3 years ago
6

Which equations represent the asymptotes of the hyperbola (x-1)^2/36-(y-2)^2/64=1 ?

Mathematics
1 answer:
allochka39001 [22]3 years ago
5 0

Answer:

4x+3y=10 and  4x-3y=-2

Step-by-step explanation:

The asymptote equation of a translate hyperbola with equation \frac{(x-h)^2}{b^2}-\frac{(y-k)^2}{a^2}=1 is y=\pm\frac{b}{a}(x-h)+k

The given hyperbola has equation: \frac{(x-1)^2}{36}-\frac{(y-2)^2}{64}=1

Or \frac{(x-1)^2}{6^2}-\frac{(y-2)^2}{8^2}=1

Comparing to \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

We have  a=6 and b=8, h=1 and k=2.

We substitute this values to get:

y=\pm\frac{6}{8}(x-1)+2

y=\pm\frac{4}{3}(x-1)+2

3y=\pm4(x-1)+6

We split the plus or minus sign to get:

3y=4x-4+6

3y=4x+2

3y-4x=2

Or

3y=-4(x-1)+6

3y=-4x+4+6

3y+4x=10

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