Question 456947: find the "a","b", orientation and write the equation of the ellipse, given: center (4,-4) vertex (9,-4) co-vertex (4,-1)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the "a","b", orientation and write the equation of the ellipse, given: center (4,-4) vertex (9,-4) co-vertex (4,-1)
**
From (x,y) coordinates of given center (4,-4) and vertex (9,-4), it can be seen that this equation of an ellipse has horizontal major axis. (x changes but y does not). Standard form for this equation: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)
..
a= distance from center to a vertex on the y=-4 line=9-4=5
a^2=25
..
b= distance from center to one end point of minor axis on the x=4 line=4-1=3
b^2=9
..
Equation: (x-4)^2/25+(y+4)^2/9
see graph below as a visual check on answers
...
y=±(9-9(x-4)^2/25)^.5-4
|
|
|
