9x^2+16y^2-18x-64y=71

解答

9 x^{2} + 16 y^{2} - 18 x - 64 y = 71

(h, k) = (1, 2), a = 4, b = 3

求解步骤

9 x^{2} + 16 y^{2} - 18 x - 64 y = 71

将

9 x^{2} + 16 y^{2} - 18 x - 64 y = 71

改写为椭圆标准方程

\frac{( x - 1 ) ^{2}}{4 ^{2}} + \frac{( y - 2 ) ^{2}}{3 ^{2}} = 1

因此椭圆的性质为:

(h, k) = (1, 2), a = 4, b = 3

a > b

因此

a

是长半轴，

b

是短半轴

中心 (h, k) = (1, 2), 长半轴为 a = 4, 短半轴为 b = 3 的椭圆

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

x^{2} + y^{2} = 2 \cdot \frac{y}{x ^{2} + y ^{2}}

\frac{x ^{2}}{1.5869} + \frac{y ^{2}}{0.9988} = 1

x^{2} + (y - 1)^{2} + (4 + y)^{2} = 64