Question 712007: I need to write an equation for a hyperbola that has the vertices (-4,1) and (-4,9) and foci at (-4,5+-rad97)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I need to write an equation for a hyperbola that has the vertices (-4,1) and (-4,9) and foci at (-4,5±√97)
**
Given hyperbola has a vertical transverse axis.
Its standard form: , (h,k)=(x,y) coordinates of center.
..
x-coordinate of center=-4
y-coordinate of center=5 (midpoint between 1 and 9)
center: (-4,5)
length of transverse axis=8 (from 1 to 9)=2a
a=4
a^2=16
..
c=√97 (distance from center to foci)
c^2=97
c^2=a^2+b^2
b^2=c^2-a^2=97-16=81
Equation of given hyperbola:
|
|
|
