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^{2} + y^{2} = 16

9 x^{2} + 4 y^{2} + 36 x - 24 y + 36 = 0

y = - \frac{x ^{2}}{10} + \frac{9 x}{10} + \frac{11}{5}

\frac{x ^{2}}{4} - \frac{y ^{2}}{4} = 1

y^{2} = 6 x

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