My mind has Hyperbola ebola and can't understand this question. Please help and explain your steps to cure it!

Write the equation of the hyperbola described below

center(3,3) ,focus(8,3), vertex (6,3)

Remember please put in the steps as well!

Thank you!!!

dom6547
Apr 2, 2018

#1**+2 **

Since the center, focus, and vertex all lie on the line \(y=3\), the hyperbola opens left/right. This means that we use this form:

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

Now, we substitute the values as follows:

1. **h** is the x-coordinate of the center

2. **k** is the y-coordinate of the center

3. **a** is the distance from the center to the vertex

4. **b ^{2}** = c

Which means:

1. \(h=3\)

2. \(k=3\)

3. \(a=\sqrt{(3-6)^2+(3-3)^3}=3\)

4. \(c=\sqrt{(3-8)^2+(3-3)^2}=5\), \(b^2=25-9=16\)

Substituting, we get \({(x-3)^2\over9}-{(y-3)^2\over16}=1\), and that is your equation.

Mathhemathh
Apr 3, 2018