Question

Which is the equation of an asymptote of the hyperbola whose equation is

(x - 2)²/4 (y - 1)²/36 = 1?

A. y = −3x − 5

B. y = −3x − 7

C. y = 3x − 5

D. y = 3x + 7

Answer 1

Answer:

C. y = 3x - 5

Step-by-step explanation:

Given the general equation of a hyperbola:

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

The equation for the asymptote line is given by:

$y=k+\frac{b}{a} (x-h)$

In your problem, we have

$\frac{(x-2)^{2} }{4}-\frac{(y-1)^{2} }{36}=1$

we have:

h=2,

k=1

a²=4 --> a=2,    im just taking the squareroot

b²=36 --> b=6

put it into your equation

$y=k+\frac{b}{a} (x-h)$

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

y = 1 + 3(x-2)

y = 1 + 3x - 6

y = 3x - 5

Answer 2

Answer:C  y=3x-5

Step-by-step explanation:

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