leitkurve y=x^2-10000x-24000000

Lösung

leitkurve

y = x^{2} - 10000 x - 24000000

y = - \frac{196000001}{4}

Schritte zur Lösung

Rewrite

y = x^{2} - 10000 x - 24000000

in the standard form

4 \cdot \frac{1}{4} (y - (- 49000000)) = (x - 5000)^{2}

(h, k) = (5000, - 49000000), p = \frac{1}{4}

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

(5000, - 49000000)

y-coordinate

y = - 49000000 - p

y = - 49000000 - \frac{1}{4}

Fasse zusammen

y = - \frac{196000001}{4}

d i rec t r i x (x + 2)^{2} = 4 (2 - y)

d i rec t r i x y^{2} - 8 x - 4 y - 20 = 0

d i rec t r i x y = - \frac{1}{2} x^{2} - 2 x + 6

d i rec t r i x y^{2} - 2 y - 8 x - 39 = 0

d i rec t r i x (x - 3)^{2} = y - 7