SOLUTION: Graph each ellipse and clearly indicate the center, foci, vertices, and co-vertices x^2/16 - x/4 + y^2/9 + 4y/9 = 11/16 PS This is on fractions!! Thank you!'

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Graph each ellipse and clearly indicate the center, foci, vertices, and co-vertices x^2/16 - x/4 + y^2/9 + 4y/9 = 11/16 PS This is on fractions!! Thank you!'      Log On


   



Question 1091493: Graph each ellipse and clearly indicate the center, foci, vertices, and co-vertices
x^2/16 - x/4 + y^2/9 + 4y/9 = 11/16
PS This is on fractions!! Thank you!'

Found 3 solutions by Alan3354, MathLover1, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
dl the FREE graph software at
www.padowan.dk
-----
Use F6 to enter this one.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2F16+-+x%2F4+%2B+y%5E2%2F9+%2B+4y%2F9+=+11%2F16 ..........complete squares

%281%2F16%29%28x%5E2+-+4x%29%2B%281%2F9%29%28+y%5E2+%2B+4y%29+=+11%2F16











%281%2F16%29%28x+-+2%29%5E2%2B%281%2F9%29%28+y+%2B+2%29%5E2+=+199%2F144


%289%2F199%29%28x+-+2%29%5E2%2B%2816%2F199%29%28+y+%2B+2%29%5E2+=1

%28x+-+2%29%5E2%2F%28199%2F9%29%2B%28+y+%2B+2%29%5E2%2F%28199%2F16%29+=1

->h=2 and k=-2, so the center is at (2, -2)
semi-major axis length:
a=sqrt%28199%2F9%29+=sqrt%28199%29%2F3a=4.7
semi-minor axis length:+b=sqrt%28199%2F16%29+=sqrt%28199%29%2F4b=3.5
c%5E2=a%5E2-b%5E2
c%5E2=199%2F9-199%2F16
c%5E2=1393%2F144
c=sqrt%281393%2F144%29
c=sqrt%281393%29%2F12
foci: (h+-+c, k) =(2+-+sqrt%281393%29%2F12, -2) ≈ (-1.1, -2)
and
foci :(h+%2Bc, k) =(2+%2Bsqrt%281393%29%2F12,+-2) ≈ (5.1,+-2)
vertices:
The vertices are a+=+sqrt%28199%29%2F3 units above and below the center, at
(2+-+sqrt%28199%29%2F3, -2) ≈ (-2.7, -2)
and
(2+%2B+sqrt%28199%29%2F3, -2) ≈ (6.7, -2)
The co-vertices are b+=+sqrt%28199%29%2F4 units to either side of the center, at
(2%2Bsqrt%28199%29%2F4 , -2) and (2-sqrt%28199%29%2F4, -2)



Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

Center: (2,-2) where the black lines (the ellipse's axes of symmetry) cross
red%28Vertices%29: U%282-sqrt%28199%29%2F3%2C-2%29 , : R%282%2C-2-sqrt%28199%29%2F4%29 , S%282%2C-2%2Bsqrt%28199%29%2F4%29
approximately (2,-5.527) and (2,1.527)
green%28foci%29: E%282-sqrt%281393%29%2F12%2C-2%29 , F%282%2Bsqrt%281393%29%2F12%2C-2%29
approximately (-1.110,-2) and (5.110,-2).