What is the foci y=(5x-7)^2-13 ?

The foci y=(5x-7)^2-13 is (7/5 ,-1299/100)

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foci y=(5x-7)^2-13

foci

(\frac{7}{5}, - \frac{1299}{100})

Solution steps

Rewrite

y = (5 x - 7)^{2} - 13

in the standard form:

4 \cdot \frac{1}{100} (y - (- 13)) = (x - \frac{7}{5})^{2}

(h, k) = (\frac{7}{5}, - 13), p = \frac{1}{100}

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

p

from the center

(\frac{7}{5}, - 13)

along the y-axis

(\frac{7}{5}, - 13 + p)

= (\frac{7}{5}, - 13 + \frac{1}{100})

Refine

(\frac{7}{5}, - \frac{1299}{100})