What is the foci x=y^2-y-42 ?

The foci x=y^2-y-42 is (-42, 1/2)

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foci x=y^2-y-42

foci

x = y^{2} - y - 42

(- 42, \frac{1}{2})

Solution steps

Rewrite

x = y^{2} - y - 42

in the standard form

4 \cdot \frac{1}{4} (x - (- \frac{169}{4})) = (y - \frac{1}{2})^{2}

(h, k) = (- \frac{169}{4}, \frac{1}{2}), p = \frac{1}{4}

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

p

from the center

(- \frac{169}{4}, \frac{1}{2})

along the x-axis

(- \frac{169}{4} + p, \frac{1}{2})

= (- \frac{169}{4} + \frac{1}{4}, \frac{1}{2})

Refine

(- 42, \frac{1}{2})

y = - 0.1 (x + 12.58)^{2} + 6.37

8 x^{2} + 1

y = - 2 x^{2} - 3

(x - 3)^{2} = - 8 (y - 4)

- 2 x^{2} + 6 x - 3