Question

Which is the equation of an asymptote of the hyperbola whose equation is 5E%7B2%7D%20%7D%7B4%7D%20-%5Cfrac%7B%28y-1%29x%5E%7B2%7D%20%7D%7B36%7D" id="TexFormula1" title="\frac{(x-2)x^{2} }{4} -\frac{(y-1)x^{2} }{36}" alt="\frac{(x-2)x^{2} }{4} -\frac{(y-1)x^{2} }{36}" align="absmiddle" class="latex-formula">= 1?
y = −3x − 5

y = −3x − 7

y = 3x − 5

y = 3x + 7

Answer 1

The equation of the asymptote is y = 3x - 5. The correct answer is option C

What is Asymptote of an Hyperbola ?

The distance from a point and the distance to a line in hyperbola is known as asymptote. The general equation is $x^{2}/ a^{2} - y^{2}/b^{2} = 1$

From the given equation of hyperbola, which is

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

The center (h , k) of the hyperbola = C(2, 1)

a = 2

b = 6

Where C = $\sqrt{a^{2} + b^{2} }$

C = $\sqrt{4 + 36}$

C = $\sqrt{40}$

C = $2\sqrt{10}$

The equation of the asymptote will be y - K = +/-(b/a)(x - h)

That is,

y - 1 = +/-(6/2)(x - 2)

y - 1 = +/-3(x - 2)

y - 1 = +/-3x - 6

y = +/-3x - 6 + 1

y = +/- 3x - 5

Therefore, the equation of the asymptote is y = 3x - 5.

Learn more about Asymptote here: brainly.com/question/4138300

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