SOLUTION: Direction: Write an equation for each hyperbola. vertices: (1,1) and (1,-3) foci: {1, -1 +or- sqrt(5)} I would like to say please and thank you for helping me, in advanc

Question 598440: Direction: Write an equation for each hyperbola.
vertices: (1,1) and (1,-3)
foci: {1, -1 +or- sqrt(5)}

I would like to say please and thank you for helping me, in advance.(:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Direction: Write an equation for each hyperbola.
vertices: (1,1) and (1,-3)
foci: {1, -1 +or- sqrt(5)}
**
This is a hyperbola with vertical transverse axis.
Its standard form of equation: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola:
x-coordinate of center=1
y-coordinate of center=(1-3)/2=-2/2=-1 (by midpoint formula)
center: (1,-1)
length of vertical transverse axis=4 (-3 to 1)=2a
a=2
a^2=4
Given coordinates of Foci: (1,-1�√5)=(1,-1�c)
c=√5
c^2=5
c^2=a^2+b^2
b^2=c^2-a^2=5-4=1
Equation:
(y+1)^2/4-(x-1)^2/1=1
RELATED QUESTIONS
Direction: Write an equation for each hyperbola. vertices: (1,-1) and (1,-9)... (answered by lwsshak3)

Write an equation for the hyperbola with vertices (-10, 1) and (6,1) and foci (-12, 1)... (answered by galactus)

Can someone show me how to do these two problems please? 1:Write an equation for the... (answered by lwsshak3)

Can you please show me how to write an hyperbola equation with foci (o,-2) and (0,2) and... (answered by lwsshak3)

Write an equation of the hyperbola with foci (0, -2) and (0, 2) and vertices of (0,-1 )... (answered by stanbon)

1. find the vertices and foci of the hyperbola x^2-y^2=1 --- --- 144 9... (answered by MathLover1)

Write the equation of the hyperbola given the foci (2,-3) and (2,7), and the vertices... (answered by lwsshak3)

May I please receive assistance on these problems. Write an equation for each ellipse... (answered by ewatrrr)

Write an equation for the hyperbola with vertices (4,0) and (-4,0) and asymptote... (answered by Theo)