What is the foci x-2=3(y-5)^2 ?

The foci x-2=3(y-5)^2 is (25/12 ,5)

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foci x-2=3(y-5)^2

foci

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

(\frac{25}{12}, 5)

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{12} (x - 2) = (y - 5)^{2}

(h, k) = (2, 5), p = \frac{1}{12}

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

p

from the center

(2, 5)

along the x-axis

(2 + p, 5)

= (2 + \frac{1}{12}, 5)

Refine

(\frac{25}{12}, 5)

y = (x)^{4} + 6 (x)^{2} - 1

y = 3 - 2 x - x^{2}

(y - 2)^{2} = 16 (x + 1)

6 x - 8 y + 15 - x^{2} = 0

4 x^{2} - 8 x + 1