25x^2+16y^2+100x-96y-154=0

解答

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

(h, k) = (- 2, 3), a = \frac{398}{5}, b = \frac{199}{2 2}

求解步骤

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

将

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

改写为椭圆标准方程

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{398}{5} ) ^{2}} + \frac{( y - 3 ) ^{2}}{( \frac{199}{2 2} ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (- 2, 3), a = \frac{398}{5}, b = \frac{199}{2 2}

b > a

因此

b

是长半轴，

a

是短半轴

中心 (h, k) = (- 2, 3), 长半轴为 b = \frac{199}{2 2}, 短半轴为 a = \frac{398}{5} 的椭圆

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