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第1413题:horizontal ellipse



If the major axis of an ellipse is parallel to the x-axis in a rectangular coordinate plane, we say that the ellipse is horizontal. If the major axis is parallel to the y-axis, we say that the ellipse is vertical. In a rectangular coordinate plane, where the center of a horizontal ellipse is (h,k), we have



As pictured a>b where a, one-half of the length of the major axis, is called the major radius. and b, one-half of the length of the minor axis, is called the minor radius. The equaton of this ellipse in standard form follows (  ).



A. (x+k)2a2+(y+h)2b2=1 \dfrac{(x+k)^2}{a^2}+\dfrac{(y+h)^2}{b^2}=1


B. (xk)2a2+(yh)2b2=1\dfrac{(x-k)^2}{a^2}+\dfrac{(y-h)^2}{b^2}=1


C. (x+h)2a2+(y+k)2b2=1\dfrac{(x+h)^2}{a^2}+\dfrac{(y+k)^2}{b^2}=1


D. (xh)2a2+(yk)2b2=1\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1



From 《Advanced Algebra》 , chapter 8


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