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Graph ( x - 2)^{2} /9+4(y + 2)^{2 } = 1
Solution
It is an ellipse. The standard form of the ellipse is
( x - h )^{2} /a^{2} + (y - k )^{2} / b^{2} = 1
It is an ellipse with center (h, k) and the right most & left most points are distance of away from the center and the top most & bottom most of the points are a distance of b away from the center.
The ellipse for this equation has center (2, -2) and has a = 3 & b = 1 . Note as well that to get the b .we're actually rewriting the equation as,
( x - 2 )^{2} /9 + (y + 2 )^{2} / (1/4) = 1
to get it in standard from.
Following is a sketch of the ellipse.
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