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受欢迎的 Geometry >

6x^2-6x+3y^2+3y-102=0

解答

6 x^{2} - 6 x + 3 y^{2} + 3 y - 102 = 0

解答

(h, k) = (\frac{1}{2}, - \frac{1}{2}), a = \frac{139}{2 2}, b = \frac{139}{2}

求解步骤

6 x^{2} - 6 x + 3 y^{2} + 3 y - 102 = 0

将

6 x^{2} - 6 x + 3 y^{2} + 3 y - 102 = 0

改写为椭圆标准方程

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{139}{2 2} ) ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{139}{2} ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (\frac{1}{2}, - \frac{1}{2}), a = \frac{139}{2 2}, b = \frac{139}{2}

b > a

因此

b

是长半轴，

a

是短半轴

中心 (h, k) = (\frac{1}{2}, - \frac{1}{2}), 长半轴为 b = \frac{139}{2}, 短半轴为 a = \frac{139}{2 2} 的椭圆

作图

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