What is the foci 4x^2-20x-24y+97=0 ?

The foci 4x^2-20x-24y+97=0 is (5/2 , 9/2)

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foci 4x^2-20x-24y+97=0

foci

4 x^{2} - 20 x - 24 y + 97 = 0

(\frac{5}{2}, \frac{9}{2})

Solution steps

Rewrite

4 x^{2} - 20 x - 24 y + 97 = 0

in the standard form

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

(h, k) = (\frac{5}{2}, 3), p = \frac{3}{2}

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

p

from the center

(\frac{5}{2}, 3)

along the y-axis

(\frac{5}{2}, 3 + p)

= (\frac{5}{2}, 3 + \frac{3}{2})

Refine

(\frac{5}{2}, \frac{9}{2})

y^{2} = x + 1

y = x^{2} - 4 x 3

(x + 2) (x - 2)

(y - 2)^{2} = 12 (x + 1)

y = - 3 x^{2} + 5 x