leitkurve 4x^2+10x-10

Lösung

leitkurve

4 x^{2} + 10 x - 10

y = - \frac{261}{16}

Schritte zur Lösung

Rewrite

y = 4 x^{2} + 10 x - 10

in the standard form

4 \cdot \frac{1}{16} (y - (- \frac{65}{4})) = (x - (- \frac{5}{4}))^{2}

(h, k) = (- \frac{5}{4}, - \frac{65}{4}), p = \frac{1}{16}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(- \frac{5}{4}, - \frac{65}{4})

y-coordinate

y = - \frac{65}{4} - p

y = - \frac{65}{4} - \frac{1}{16}

Fasse zusammen

y = - \frac{261}{16}

d i rec t r i x (x - 7)^{2} = - 12 (y - 1)

d i rec t r i x y^{2} = 5 y + 7 x + 3

d i rec t r i x 2 y^{2} - 12 y - x + 5 = 0

d i rec t r i x - 0.03 x^{2} + 45 x + 124.5

d i rec t r i x 4 y^{2} - 12 y + 56 x + 177 = 0