What is the foci (-20x+13)^2 ?

The foci (-20x+13)^2 is (13/20 , 1/1600)

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foci (-20x+13)^2

foci

(- 20 x + 13)^{2}

(\frac{13}{20}, \frac{1}{1600})

Solution steps

Rewrite

y = (- 20 x + 13)^{2}

in the standard form:

4 \cdot \frac{1}{1600} (y - 0) = (x - \frac{13}{20})^{2}

(h, k) = (\frac{13}{20}, 0), p = \frac{1}{1600}

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

p

from the center

(\frac{13}{20}, 0)

along the y-axis

(\frac{13}{20}, 0 + p)

= (\frac{13}{20}, 0 + \frac{1}{1600})

Refine

(\frac{13}{20}, \frac{1}{1600})

2 x^{2} + 4 x - 16

- x^{2} + 4 x

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

- \frac{1}{2} (x - 4)^{2} + 3

(x - 6)^{2} = + 8 (y - 2)