|
Question 617010: ``All of the questions are based on the same ellipse...
1)An ellpise has foci at (-5,0)and (5,0). What is the value of c²?
2)If the sum of the focal radii of this ellpise is 12, what is the value of a²?
3)Using your conclusions, what is the value of b²?
4)What is the equation of the ellipes?
5)What are the x-intercepts of the ellipse?
6)What are the y-intercepts of this ellipse?
7) Graph the ellipse and plot the foci on a graph.
please give me step by step instructions
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Given ellipse has a horizontal major axis.
Its standard form: (x-h)2/a^2+(y-k)^2/b^2=1
For given ellipse:
center:(0,0)
..
1)An ellpise has foci at (-5,0)and (5,0). What is the value of c²?
c=5
c^2=25
..
2)If the sum of the focal radii of this ellpise is 12, what is the value of a²?
focal radii=12=2a
a=6
a^2=36
..
3)Using your conclusions, what is the value of b²?
b^2=a^2-c^2=36-25=11
..
4)What is the equation of the ellipse?
x2/36+y^2/11=1
..
5)What are the x-intercepts of the ellipse?
set y=0, then solve for x
x2/36=1
x^2=36
x=±√36=±6
x-int at -6 and 6
..
6)What are the y-intercepts of this ellipse?
set x=0, then solve for y
y^2/11=1
y^2=11
y=±√11≈±3.32
y-int at -3.32 and 3.32
...
7) Graph the ellipse and plot the foci on a graph.
see graph below: (foci not shown)
y=(11-11x^2/36)^.5
|
|
|
| |
