Question 35472This question is from textbook algebra for college students
: I need help with this too, Please:
Find the vertices, the endpoints of the minor axis, and foci of the given ellipse, and sketch it's graph:
(x+5) squared + 4(y-4) squared = 16
This question is from textbook algebra for college students
Found 2 solutions by Nate, rapaljer:
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! (x+5)^2 + 4(y-4)^2 = 16 original
((x+5)^2)/16 + ((y-4)^2)/4 = 1 divide by 16 to get the side to equal 1
the major axis is the highest value (16)^(1/2)
the major axis is 4 units long, and the major axis is horizontal
the minor axis, on the other hand, is the lower value (4)^(1/2)
the minor axis is 2 units long
the center is found by: ((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1
where a is the length of the minor axis and b is the length of the minor axis and (h,k) is the center
the center is (-5,4)
...................................................................
To Graph: go to the point (-5,4) and make points 4 units left and right of that point....also, go 2 units up and down from the center....connect the dots (excluding the center) to make an ellipse
Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! 
Divide both sides of the equation by 16 in order to set it equal to 1, which is standard form for an ellipse.
From this the center of the ellipse will be at (-5,4), the major radius will be in the x direction with  so a = 4, and the minor radius will be in the y direction with  , so b = 2. Since for ellipses,  ,  so c = focal distance which is  , applied in the x direction.
From that you should be able to sketch the graph and find the vertices, foci, and other information.
R^2 at SCC
|
|
|
