What is the foci y=(x-4)(x-7) ?

The foci y=(x-4)(x-7) is (11/2 ,-2)

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foci y=(x-4)(x-7)

foci

y = (x - 4) (x - 7)

(\frac{11}{2}, - 2)

Solution steps

Rewrite

y = (x - 4) (x - 7)

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{9}{4})) = (x - \frac{11}{2})^{2}

(h, k) = (\frac{11}{2}, - \frac{9}{4}), p = \frac{1}{4}

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

p

from the center

(\frac{11}{2}, - \frac{9}{4})

along the y-axis

(\frac{11}{2}, - \frac{9}{4} + p)

= (\frac{11}{2}, - \frac{9}{4} + \frac{1}{4})

Refine

(\frac{11}{2}, - 2)

x^{2} = 8 (y + 4)

y^{2} + 4 x = 0

y = - 3 (x + 1)^{2} - 1

y = x (x - 4)

x + y^{2} = 0