What is the foci 5x(2x+4)-3x ?

The foci 5x(2x+4)-3x is (-17/20 ,-36/5)

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foci 5x(2x+4)-3x

foci

5 x (2 x + 4) - 3 x

(- \frac{17}{20}, - \frac{36}{5})

Solution steps

Rewrite

y = 5 x (2 x + 4) - 3 x

in the standard form

4 \cdot \frac{1}{40} (y - (- \frac{289}{40})) = (x - (- \frac{17}{20}))^{2}

(h, k) = (- \frac{17}{20}, - \frac{289}{40}), p = \frac{1}{40}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(- \frac{17}{20}, - \frac{289}{40})

along the y-axis

(- \frac{17}{20}, - \frac{289}{40} + p)

= (- \frac{17}{20}, - \frac{289}{40} + \frac{1}{40})

Refine

(- \frac{17}{20}, - \frac{36}{5})

x^{2} - 10 x - 12 y - 23 = 0

y = (9 x - 2) x 3

x^{2} = - 24 y

y = 12 x^{2}

(x + 3)^{2} - 2