焦点 4x^2+9y^2+3x-18y^2+37=0

解答

焦点

4 x^{2} + 9 y^{2} + 3 x - 18 y^{2} + 37 = 0

(- \frac{3}{8}, \frac{7579}{24}), (- \frac{3}{8}, - \frac{7579}{24})

求解步骤

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

计算双曲线性质

4 x^{2} + 9 y^{2} + 3 x - 18 y^{2} + 37 = 0 :

上下开口双曲线，

(h, k) = (- \frac{3}{8}, 0), a = \frac{583}{12}, b = \frac{583}{8}

(- \frac{3}{8}, 0 + c), (- \frac{3}{8}, 0 - c)

计算

c :

c = (\frac{583}{12})^{2} + (\frac{583}{8})^{2} : \frac{7579}{24}

(- \frac{3}{8}, 0 + \frac{7579}{24}), (- \frac{3}{8}, 0 - \frac{7579}{24})

整理后得

(- \frac{3}{8}, \frac{7579}{24}), (- \frac{3}{8}, - \frac{7579}{24})

f oc i 9 x^{2} - 2 y^{2} = 18

f oc i \frac{x ^{2}}{49} - \frac{y ^{2}}{36} = 1

f oc i 36 y^{2} - 4 x^{2} = 144

f oc i x^{2} - 4 y^{2} + 8 x + 16 y - 4 = 0

f oc i 5 x^{2} - 2 y^{2} + 10 x - 12 y = 23