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Over [174]
3 years ago
5

Write the equation of the hyperbola with center (2,-5), vertex (2,-2), and focus (2+-5+2sqrt3)

Mathematics
2 answers:
Mars2501 [29]3 years ago
5 0

Answer:

option A : \frac{(y+5)^2}{9} - \frac{(x-2)^2}{3}=1

Step-by-step explanation:

the equation of the hyperbola with center (2,-5), vertex (2,-2), and focus (2+-5+2sqrt3)

center is (2,-5), vertex is (2,-2). It is a vertical hyperbola

General equation for vertical hyperbola is

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

Center (2,-5) so h=2, k= -5

vertex is (2,-2)

We know vertex is (h, k+a), k=-5

k + a= -2

-5 + a = -2

so a = 3

Given  focus (2+-5+2sqrt3)

Focus is (h , k+c), k= -5

k+c= -5+2\sqrt{3}

-5+c= -5+2\sqrt{3}

Add 5 on both sides

c= 2\sqrt{3}

We need to find out b

c^2 = a^2 + b^2

(2\sqrt{3})^2= 3^2 + b^2

12 = 9 + b^2

b^2 = 3

we know a=3  so a^2 =9

we know h=2  and k = -5

Plug in all the values in general equation

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

\frac{(y+5)^2}{9} - \frac{(x-2)^2}{3}=1


UNO [17]3 years ago
3 0

Answer:

Its A for sure :)


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