What is the foci (2x-1)(5x-6) ?

The foci (2x-1)(5x-6) is (17/20 ,-6/5)

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foci (2x-1)(5x-6)

foci

(2 x - 1) (5 x - 6)

(\frac{17}{20}, - \frac{6}{5})

Solution steps

Rewrite

y = (2 x - 1) (5 x - 6)

in the standard form

4 \cdot \frac{1}{40} (y - (- \frac{49}{40})) = (x - \frac{17}{20})^{2}

(h, k) = (\frac{17}{20}, - \frac{49}{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{49}{40})

along the y-axis

(\frac{17}{20}, - \frac{49}{40} + p)

= (\frac{17}{20}, - \frac{49}{40} + \frac{1}{40})

Refine

(\frac{17}{20}, - \frac{6}{5})

20 t - t^{2}

y^{2} - 12 y - 4 x = - 28

(x - 1)^{2} = 8 (y - k)

(y - 4)^{2} = 8 (x - 3)

y = 16 x^{2} - 25