SOLUTION: find the center,vertices and foci of the ellipse: 16x^2+4y^2+64x-24y+36=0

Question 491835: find the center,vertices and foci of the ellipse:
16x^2+4y^2+64x-24y+36=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the center,vertices and foci of the ellipse:
16x^2+4y^2+64x-24y+36=0
**
16x^2+4y^2+64x-24y+36=0
complete the squares:
16(x^2+4x+4)+4(y^2-6y+9)=-36+64+36=64
16(x+2)^2+4(y-3)^2=64
divide by 64
(x+2)^2/4+(y-3)^2/16=1
This is an ellipse with a vertical major axis of the standard form:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.
..
For given problem:
Center: (-2,3)
a^2=16
a=√16=4
length of vertical major axis=2a=8
vertices: (end-points of major axis)=(-2, 3�a)=(-2, 3�4)=(-2,7) and (-2,-1)
Vertices: (-2,7) and (-2,-1)
..
b^2=4
b=√4=2
..
c^2=a^2-b^2=16-4=12
c=√12=3.46
Foci: (-2,3�c)=(-2,3�3.46)=(-2, 6.46) and (-2, -.46)
Ans:
Center: (-2,3)
Vertices: (-2,7) and (-2,-1)
Foci:(-2, 6.46) and (-2, -.46)
See graph below as a visual check on answers:
..
y=�((16-4(x+2)^2)^.5)+3

RELATED QUESTIONS
Find the minor axis vertices of the... (answered by lwsshak3)

find the center of this ellipse:... (answered by stanbon,ewatrrr)

Find the center, vertices and foci of the ellipse... (answered by lwsshak3)

Find the center, vertices, and foci of the ellipse... (answered by Fombitz)

Find the center, foci, vertices, and lengths of the major and minor axes. 16x^2 - 64x (answered by lwsshak3)

Find the ellipse 16x^2+25y^2-64x+50y-311=0, find the center, vertices, and foci, and draw (answered by Fombitz)

Find the center, vertices, and foci of each ellipse. (a.) (x+9)^2/4 + (y-18)^2/100=1 (answered by lwsshak3)

What is the center of an ellipse 16x^2+64x+y^2-4y+4=0 (answered by lwsshak3)

Find the center, vertices, foci and eccentricity of the ellipse... (answered by ikleyn)