SOLUTION: 1) Find the vertices and foci of the ellipse 4x2 + 25y2 - 16x + 100y = -16 2) Find the center and asymptotes of the hyperbola 4x2 - 9y2 - 8x - 18y = 41 3) solve the sy

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 1) Find the vertices and foci of the ellipse 4x2 + 25y2 - 16x + 100y = -16 2) Find the center and asymptotes of the hyperbola 4x2 - 9y2 - 8x - 18y = 41 3) solve the sy      Log On


   

Question 38377This question is from textbook Algebra 2 with Trig
: 1) Find the vertices and foci of the ellipse
4x2 + 25y2 - 16x + 100y = -16
2) Find the center and asymptotes of the hyperbola
4x2 - 9y2 - 8x - 18y = 41
3) solve the system x2 + y2 = 16 and x2/16 + y2/9 = 1
4) find the center and radius of the circle
x2 + y2 -4x + 2y = 4 This question is from textbook Algebra 2 with Trig

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
1) Find the vertices and foci of the ellipse
4x%5E2+%2B+25y%5E2+-+16x+%2B+100y+=+-16
4x%5E2-16x%2B25y%5E2%2B100y=-16
%284x%5E2-16x%29%2B%2825y%5E2%2B100y%29=-16
4%28x%5E2-4x%29%2B25%28y%5E2%2B4y%29=-16
4%28x-2%29%5E2%2B25%28y%2B2%29%5E2=100
%28%28x-2%29%5E2%2F25%29%2B%28%28y%2B2%29%5E2%2F4%29=1
The ellipse has a horizontal major axis. Center is (2,-2).
a=5
b=2
c%5E2=a%5E2-b%5E2
c%5E2=5%5E2-2%5E2
c%5E2=25-4
c=%2821%29%5E%281%2F2%29
Vertices: (7,-2),(-3,-2),(2,0),(2,-4)
Foci: (2-(21)^(1/2),-2),(2+(21)^(1/2),-2)
2) Find the center and asymptotes of the hyperbola
4x2 - 9y2 - 8x - 18y = 41
4x%5E2-8x-9y%5E2-18y=41
%284x%5E2-8x%29%2B%28-9y%5E2-18y%29=41
4%28x%5E2-2x%29-9%28y%5E2%2B2y%29=41
4%28x-1%29%5E2-9%28y%2B1%29%5E2=36
%28%28x-1%29%5E2%2F9%29-%28%28y%2B1%29%5E2%2F4%29=1
This hyperbola has a horizontal transverse axis. The center is (1,-1). The slope of the asymptotes is b/a or -b/a. a=3 and b=2
y%2B1=%282%2F3%29%28x-1%29 or y%2B1=%28-2%2F3%29%28x-1%29
3) solve the system x^2 + y^2 = 16 and x^2/16 + y^2/9 = 1
for x%5E2+%2B+y%5E2+=+16, y%5E2+=+-x%5E2+%2B+16
Plug in: x%5E2%2F16+%2B+y%5E2%2F9+=+1
144%28x%5E2%2F16%29+%2B+144%28%28-x%5E2+%2B+16%29%2F9%29+=+144%281%29
9x%5E2+%2B+16%28-x%5E2+%2B+16%29+=+144
9x%5E2+-+16x%5E2+=+-112
-7x%5E2+=+-112
x%5E2+=+16
x+=+%284%29+or+%28-4%29
Plug in:
x%5E2+%2B+y%5E2+=+16
%284%29%5E2+%2B+y%5E2+=+16
y%5E2+=+0
y+=+0
(4,0) and (-4,0) are your answers
4) find the center and radius of the circle
x%5E2+%2B+y%5E2+-4x+%2B+2y+=+4
x%5E2+-+4x+%2B+y%5E2+%2B+2y+=+4
%28x%5E2+-+4x%29+%2B+%28y%5E2+%2B+2y%29+=+4
%28x+-+2%29%5E2+%2B+%28y+%2B+1%29%5E2+=+9
The center is (2,-1) and the radius is 3.