What is the foci x^{(2)}-6x+5y=-34 ?

The foci x^{(2)}-6x+5y=-34 is (3,-25/4)

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foci x^{(2)}-6x+5y=-34

foci

x^{(2)} - 6 x + 5 y = - 34

(3, - \frac{25}{4})

Solution steps

Rewrite

x^{2} - 6 x + 5 y = - 34

in the standard form

4 (- \frac{5}{4}) (y - (- 5)) = (x - 3)^{2}

(h, k) = (3, - 5), p = - \frac{5}{4}

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

p

from the center

(3, - 5)

along the y-axis

(3, - 5 + p)

= (3, - 5 + (- \frac{5}{4}))

Refine

(3, - \frac{25}{4})

x (2 x + 3)

6 x^{2} - 49

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

(x - 3)^{2} = - 4 (y - 1)

- (x - 1)^{2}