SOLUTION: Find the standard form, graph, and find the asymptotes of the hyperbola Verticies:(-10,3), (6,3). Focus: (-12,3), (8,3)

Question 616738: Find the standard form, graph, and find the asymptotes of the hyperbola
Verticies:(-10,3), (6,3). Focus: (-12,3), (8,3)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the standard form, graph, and find the asymptotes of the hyperbola
Verticies:(-10,3), (6,3). Focus: (-12,3), (8,3)
**
Given hyperbola has a horizontal transverse axis.
Its standard form of equation: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center.
center: (-2,3)
length of horizontal transverse axis=16=2a
a=8
a^2=64
..
2c=20
c=10
c^2=100
..
c^2=a^2+b^2
b^2=c^2-a^2=100-64=36
b=√36=6
..
Equation of given hyperbola:
(x+2)^2/64-(y-3)^2/36=1
..
slopes of asymptotes for hyperbolas with horizontal transverse axis=�b/a=�6/8=�3/4
asymptotes are straight lines that intersect at center: y=mx+b, m=slope, b=y-intercept
..
Equation for asymptote with negative slope: y=-3x/4+b
solve for b using coordinates of center.
3=(-3*-2)/4+b
b=-3/2
equation: y=-3x/4+3/2
..
Equation for asymptote with positive slope: y=3x/4+b
solve for b using coordinates of center.
3=(3*-2)/4+b
b=9
equation: y=3x/4+9/2
..
see graph below:
y=�((36(x+2)^2/64)-36)^.5+3

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