What is 4x^{(2)}-20x-24y+97=0 ?

The solution to 4x^{(2)}-20x-24y+97=0 is Parabola with (h,k)=(5/2 ,3),p= 3/2

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

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

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

Solution steps

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

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}

Therefore parabola properties are:

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

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

2 y^{2} - 12 y - x + 19 = 0

(y - 3)^{2} = 12 (x + 4)

(y - 3)^{2} = 12 (x + 6)

y^{2} + 4 x - 12 = 0

What is 4x^{(2)}-20x-24y+97=0 ?
The solution to 4x^{(2)}-20x-24y+97=0 is Parabola with (h,k)=(5/2 ,3),p= 3/2