Question

Write an equation for the hyperbola.

Vertices at ( -5,2) and (-1,2), passing through the point (-6,4)

Could you be so nice and help me please:)
I have still wrong answer and I have no idea where I'm doing mistake.

My work:
Horizontal transverse )(
Center (-3,2)
a= 2

(-6)^2/2^2 -(4)^2/b^2=1

b^2 =2
Substitute (h,k)= (-3,2), a =4, b=2

But my answer is wrong.
Correct solution is (x+3)^2/4-(y-2)^2/(16/5)=1

Thank you so much for help:))

Answer 1

you got the center right, so the equation must be

(x+3)^2/a^2 - (y-2)^2/b^2 = 1

Since a=2, and (-6,4) is on the graph, so

9/4 - 4/b^2 = 1
b^2 = 16/5

(x+3)^2/4 - (y-2)^2/(16/5) = 1

As you can see, it works:

http://www.wolframalpha.com/input/?i=plot+%28x%2B3%29^2%2F4+-+%28y-2%29^2%2F%2816%2F5%29+%3D+1%2C+y%3D4%2C+x+%3D+-6