Question 475138
I need be able to find the center, vertices, and foci of the ellipse with the equation 4x2 + y2 - 8x + 4y - 8 = 0.. I can't seem to get it right!I need be able to find the center, vertices, and foci of the ellipse with the equation 4x2 + y2 - 8x + 4y - 8 = 0.. I can't seem to get it right!
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f(x)=4x2+y2-8x+4y-8=0
completing the squares
4(x^2-2x+1)+(y^2+4y+4)-8-4-4=0
4(x-1)^2+(y+2)^2=16
divide by 16
(x-1)^2/4+(y+2)^2/16=1
This is an ellipse with vertical major axis of 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.
..
Center:(1,-2)
a^2=16
a=4
length of major axis=2a=8
vertices: (1,-2±a)=(1,-2±4)=(1,-6) and (1,2)
..
b^2=4
b=2
..
c^2=a^2-b^2=16-4=12
c√12
Foci: (1,-2±c)=(1,-2±√12)=(1,1.46) and (1,-5.46)