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Question 676440: I need the general equation for this ellipse and its major axis.
4x^2+y^2+4y=0
Answer by khurshidi(7)   (Show Source):
You can put this solution on YOUR website! I need the general equation for this ellipse and its major axis.
4x^2+y^2+4y=0
Solution:
4x^2 + y^2 + 4y = 0
or
4x^2 + 0x + y^2 + 4y = 0 -------->(1)
Adding '4' on both sides in (1)
4x^2 + 2(4x)(0) + 0^2 + y^2 + 4y + 4 = 4
or
4(x + 0)^2 + (y + 2)^2 = 4
or
4(x + 0)^2/4 + (y + 2)^2/4 = 1
or
(x + 0)^2/1 + (y + 2)^2/4 = 1
or
(x + 0)^2/1^2 + (y + 2)^2/2^2 = 1 -------->(2)
Compare (2) with general equation of the ellipse
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
we get
Center(h, k) = (0, -2)
since
b > a
i.e. 2 > 1
therefore major axis along y-axis
thus
c^2 = b^2 - a^2 = 2^2 - 1^2 = 4 - 1 = 3
c^2 = 3
or
c = (+-)sqrt(3)
Thus
foci(h, k(+-)c) = (0, -2(+-)sqrt(3))
langht of major axis = 2b = 2 * 2 = 4
Hence
Equation (2) is the general equation of the given ellipse with center C(h, k) = (0, -2) and its major axis is along y-axis and length of major axis is 4units.
Hope the answer your question
Regards,
Khurshidi
http://sscom.netai.net
http://facebook.com/SSCOMMathemagics
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