Question 668117: the question says, "identify each curve. find the characteristics listed."
y^2/16 - x^2/9 =1. center asymptote foci
x^2/64 + y^2/16 = 1. center vertices foci
someone help please, this is very confusing
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! the question says, "identify each curve. find the characteristics listed."
y^2/16 - x^2/9 =1. center asymptote foci
x^2/64 + y^2/16 = 1. center vertices foci
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find: center, asymptote, foci
y^2/16-x^2/9 =1
This is an equation of a hyperbola with vertical transverse axis.
Its standard form: , (h,k)=(x,y) coordinates of center
For given equation: y^2/16-x^2/9 =1
center: (0,0)
a^2=16
a=√16=4
b^2=9
b=√9=3
Foci:
c^2=a^2+b^2=16+9=25
c=√25=5
Foci=(0,5) and (0,-5)
asymptotes are straight lines that go thru the center and are of the form: y=mx+b, m=slope, b=y-intercept
slopes of asymptotes for hyperbolas with vertical transverse axis=±a/b=±4/3
Equations of asymptotes:
y=-4x/3
and
y=4x/3
...
find: center, vertices, foci
x^2/64 + y^2/16 = 1
This is an equation of an ellipse with horizontal major axis axis.
Its standard form: , (h,k)=(x,y) coordinates of center
For given equation: x^2/64+y^2/16=1
center: (0,0)
a^2=64
a=√64=8
vertices: (0,8) and (0,-8)
b^2=16
b=√16=4
Foci:
c^2=a^2-b^2=64-16=48
c=√48
Foci=(0,√48) and (0,-√48)
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