x^2+4y^2-6x+16y+21=0

解答

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0

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

求解步骤

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0

将

x^{2} + 4 y^{2} - 6 x + 16 y + 21 = 0

改写为椭圆标准方程

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

因此椭圆的性质为:

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

a > b

因此

a

是长半轴，

b

是短半轴

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

x^{2} + y^{2} - 6 x + 4 y + 9 = 0

f (x) = x^{2} - 4 x + 3

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y - k ) ^{2}}{b ^{2}} = 1

x^{2} + y^{2} + 4 x - 6 y - 3 = 0

\frac{x ^{2}}{25} - \frac{y ^{2}}{4} = 1