What is the foci y=(3x-4)(4x-3)-2x ?

The foci y=(3x-4)(4x-3)-2x is (9/8 ,-19/6)

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foci y=(3x-4)(4x-3)-2x

foci

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

(\frac{9}{8}, - \frac{19}{6})

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{48} (y - (- \frac{51}{16})) = (x - \frac{9}{8})^{2}

(h, k) = (\frac{9}{8}, - \frac{51}{16}), p = \frac{1}{48}

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

p

from the center

(\frac{9}{8}, - \frac{51}{16})

along the y-axis

(\frac{9}{8}, - \frac{51}{16} + p)

= (\frac{9}{8}, - \frac{51}{16} + \frac{1}{48})

Refine

(\frac{9}{8}, - \frac{19}{6})

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

- 2 x^{2} + 24 x + y - 70 = 0

y = - 4 x^{2} + 1

x^{2} - 20 y - 2 x - 39 = 0

y^{2} + x + y = 0