Question

Write the equation of the hyperbola. Foci: (-3,0), (1,0) Vertices: (-2,0), (0,0)

Answer 1

yikes these are endless

Answer 2

the center is half way between the vertices, so it must be \((-1,0)\)

Answer 3

that means it is going to look like
\[\frac{(x+1)^2}{a^2}-\frac{y^2}{b^2}=1\] now we need \(a\) and \(b\)

Answer 4

the vertex is one unit from the center, so \(a=1\) and of course \(a^2=1\)

Answer 5

the focus is 2 units from the center so \(c=2\) and \(b^2=2^1-1^2=3\)

Answer 6

final answer is
\[(x+1)^2-\frac{y^2}{3}=1\]

Answer 7

wow thank you so much, you have no idea how much this helps me

Answer 8

yw, again all you really need to do is look here
http://www.purplemath.com/modules/hyperbola3.htm
and follow along making the necessary changes with the numbers

Answer 9

ill try that :)

Answer 10

you can check the answer here
http://www.wolframalpha.com/input/?i=hyperbola+%28x%2B1%29^2-y^2%2F3%3D1