SOLUTION: find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4)

Question 751431: find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4)
hyperbola has a vertical transverse axis.
Its standard form of equation: , (h,k)=(x,y) coordinates of the center
For given hyperbola:
x-coordinate of center=2
y-coordinate of center=1 (midpoint of vertical transverse axis)
center: (2,1)
a=2 (distance from center to vertices)
a^2=4
c=5 (distance from center to foci)
c^2=25
c^2=a^2+b^2
b^2=c^2-a^2=25-4=21
Equation of given hyperbola:

RELATED QUESTIONS
Find the equation of the hyperbola with vertices at (-4,2) and (0,2) and foci at (-5,2) (answered by Edwin McCravy)

Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at... (answered by lwsshak3)

Write an equation of the hyperbola that meets the following conditions: the vertices... (answered by josgarithmetic)

Write an equation of a hyperbola with vertices (3 - sqrt[2], 4) and (3 + sqrt[2], 4) and... (answered by ewatrrr)

6. find the center, vertices, and foci of the ellipse with the following equation: (answered by lynnlo)

find an equation of the hyperbola with vertices at (-6, 1) and (4, 1) and foci at (-8, 1) (answered by lwsshak3)

find the center, eccentrics with vertices at (2, 1) and (2, -5); foci at (2, 3) and (2,... (answered by ikleyn)

For the hyperbola represented by [(y+2)^2]/4 - [x^2]/12=1 find the foci and... (answered by lwsshak3)

Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by Edwin McCravy)