|
Question 442712: 16x^2 + 9y^2 - 32x + 18y + 9 = 128
how do you write in standard form, find foci, and asymptotes?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 16x^2 + 9y^2 - 32x + 18y + 9 = 128
how do you write in standard form, find foci, and asymptotes
..
completing the squares
16(x^2-2x+1)+9(y^2+2y+1)=128-9+16+9=144
(x-1)^2/9+(y+1)^2/16=1
This is an ellipse with center at (1,-1) and vertical major axis.
Because it is an ellipse, asymptotes do no apply
Standard form of an ellipse with vertical major axis:
(y-k)^2/a^2+(x-h)^2/b^2=1< with (h,k) being the (x,y) coordinates of the center. (a>b)
For given equation:
center(1,-1)
a^2=16
a=4 (length of major axis)
b^2=9
b=3 (length of minor axis)
c^2=a^2-b^2=16-9=7
c=√7=2.65 (distance from ctr to foci on major axis.
foci(1,-1+-2.65)
see graph of the ellipse below
..
y=((1-(x-1)^2/9))*16))^.5-1
|
|
|
| |
