SOLUTION: 4x^2+10y^2-16x+40y+16=0 How do i find the center and foci?

Question 456433: 4x^2+10y^2-16x+40y+16=0 How do i find the center and foci?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
4x^2+10y^2-16x+40y+16=0 How do i find the center and foci?
..
4x^2+10y^2-16x+40y+16=0
completing the square
4x^2-16x+10y^2+40y=-16
4(x^2-4x+4)+10(y^2+4+4)=-16+16+40
4(x-2)^2+10(y+2)^2=40
(x-2)^2/10+(y+2)^2/4=40
This equation is an ellipse with center at (2,-2), with a horizontal major axis.
..
Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
The difference between the two forms is the interchange of a^2 and b^2.
..
For given equation:
a^2=10
b^2=4
c^2=a^2-b^2=10-4=6
c=√6
foci is at (2�√6,-2)
See the graph below as a visual check on the answer:
..
y=(4-4(x-2)^2/10)^.5-2

RELATED QUESTIONS
16x^2 + 25y^2 - 96x - 200y + 144 = 0 find the center, foci, and... (answered by lwsshak3)

x^2+4x+4-4y^2+8y-8=0 Is this an equation for a hyperbola? How do I find the center,... (answered by Edwin McCravy)

Find the center,foci, vertices and lengh\th of the axes for the ellipse... (answered by KMST)

Find the center, vertices, foci and eccentricity of the ellipse 6x^2 + 2y^2 + 18x - 10y + (answered by ikleyn)

find center, foci, vertices, and asymptotes of the hyperbola. 16x^2-9y^2-96y+144=0... (answered by solver91311)

how do i find center and foci of (x^2)/9 + (y^2)/12 = 1? Is the center... (answered by josgarithmetic)

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

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

What is the standard form of... (answered by MathLover1)