焦点 4x^2-8y^2=3

解答

焦点

4 x^{2} - 8 y^{2} = 3

(\frac{3}{2 2}, 0), (- \frac{3}{2 2}, 0)

求解步骤

(h + c, k), (h - c, k)

计算双曲线性质

4 x^{2} - 8 y^{2} = 3 :

左右开口双曲线，

(h, k) = (0, 0), a = \frac{3}{2}, b = \frac{3}{2 2}

(0 + c, 0), (0 - c, 0)

计算

c :

c = (\frac{3}{2})^{2} + (\frac{3}{2 2})^{2} : \frac{3}{2 2}

(0 + \frac{3}{2 2}, 0), (0 - \frac{3}{2 2}, 0)

整理后得

(\frac{3}{2 2}, 0), (- \frac{3}{2 2}, 0)

f oc i \frac{y ^{2}}{1600} - \frac{x ^{2}}{5625} = 1

f oc i \frac{( x + 2 ) ^{2}}{64} - \frac{( y - 3 ) ^{2}}{36} = 1

f oc i \frac{( y + 2 ) ^{2}}{25} - \frac{( x + 4 ) ^{2}}{9} = 1

f oc i (\frac{x - 6}{4})^{2} - (\frac{y}{4})^{2} = 1

f oc i 25 y^{2} - 4 x^{2} = 100