SOLUTION: Find the center, foci, vertices, and asymptotes. Please show all your steps. y^2/25-x^2=1

Question 636453: Find the center, foci, vertices, and asymptotes. Please show all your steps.
y^2/25-x^2=1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the center, foci, vertices, and asymptotes. Please show all your steps.
y^2/25-x^2=1
**
This is a hyperbola with vertical transverse axis.
Its standard form of equation , (h,k)=(x,y) coordinates of center
..
For given equation of a hyperbola:
center: (0,0)
..
a^2=25
a=√25=5
vertices: (0, 0�a)=(0, 0�5)=(0,-5) and (0,5)
..
b^2=1
b=1
..
c^2=a^2+b^2=25+1=26
c=√26≈5.1
Foci: (0, 0�c)=(0, 0�5.1)=(0,-5.1) and (0,5.1)
..
Asymptotes are lines that intersect at center (0,0). Equation: y=mx+b, m=slope, b=y-intercept
slopes of asymptotes of hyperbolas with vertical transverse axis=�a/b=�5/1=�5
Equation of asymptote with negative slope (-5)
y=-5x+b
y=-5x+0
y=-5x
..
Equation of asymptote with positive slope (5)
y=5x+b
y=5x+0
y=5x

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