What is the foci y=(6x+7)^2 ?

The foci y=(6x+7)^2 is (-7/6 , 1/144)

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foci y=(6x+7)^2

foci

y = (6 x + 7)^{2}

(- \frac{7}{6}, \frac{1}{144})

Solution steps

Rewrite

y = (6 x + 7)^{2}

in the standard form:

4 \cdot \frac{1}{144} (y - 0) = (x - (- \frac{7}{6}))^{2}

(h, k) = (- \frac{7}{6}, 0), p = \frac{1}{144}

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

p

from the center

(- \frac{7}{6}, 0)

along the y-axis

(- \frac{7}{6}, 0 + p)

= (- \frac{7}{6}, 0 + \frac{1}{144})

Refine

(- \frac{7}{6}, \frac{1}{144})

\frac{x ^{2}}{16}

y^{2} = 16 x - 8

(x - 6)^{2}

\frac{x ^{2}}{2} + 1

(y + 3)^{2} = 48 (x - 5)