|
Question 618962: Find the equations of the asymptotes of the hyperbola.
25y^2 - 16x -400 = 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the equations of the asymptotes of the hyperbola.
25y^2 - 16x^2 -400 = 0
25y^2-16x^2=400
Divide by 400
y^2/16-x^2/25=1
This is an equation of a hyperbola with vertical transverse axis
Its form of equation: (y-k)^2/a^2-(x-h)^2=1, (h,k)=(x,y) coordinates of the center.
For given equation:
center: (0,0)
a^2=16
a=√16=4
b^2=25
b=√25=5
..
Asymptotes are straight lines that intersect at the center(0,0). Equation: y=mx+b, m=slope, b=y intercept
Slopes of asymptotes for hyperbolas with vertical transverse axis=a/b=4/5
Equation of asymptote with slope<0
y=-4x/5+b
since asymptote go thru center, y-intercept, b=0
so, equation: y=-4x/5
..
By the same reasoning,
Equation of asymptote with slope>0
y=4x/5
|
|
|
| |
