(x^2)/(C1^2)=1-(y^2)/(C2^2)

解答

\frac{x ^{2}}{C 1 ^{2}} = 1 - \frac{y ^{2}}{C 2 ^{2}}

(h, k) = (0, 0), a = C, b = 2 C

求解步骤

\frac{x ^{2}}{C \cdot 1 ^{2}} = 1 - \frac{y ^{2}}{C \cdot 2 ^{2}}

将

\frac{x ^{2}}{C 1 ^{2}} = 1 - \frac{y ^{2}}{C 2 ^{2}}

改写为椭圆标准方程

\frac{( x - 0 ) ^{2}}{( C ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 C ) ^{2}} = 1

因此椭圆的性质为:

(h, k) = (0, 0), a = C, b = 2 C

a > b

因此

a

是长半轴，

b

是短半轴

中心 (h, k) = (0, 0), 长半轴为 a = C, 短半轴为 b = 2 C 的椭圆

\frac{( x - 1 ) ^{2}}{169} + \frac{( y - 4 ) ^{2}}{144} = 1

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

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

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{25} = 1

4 x^{2} - 16 x + 9 y^{2} + 54 y + 61 = 0