What is 2x^2+4x^2-3x+9y+24=0 ?

The solution to 2x^2+4x^2-3x+9y+24=0 is Parabola with (h,k)=(1/4 ,-21/8),p=-3/8

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2x^2+4x^2-3x+9y+24=0

2 x^{2} + 4 x^{2} - 3 x + 9 y + 24 = 0

(h, k) = (\frac{1}{4}, - \frac{21}{8}), p = - \frac{3}{8}

Solution steps

2 x^{2} + 4 x^{2} - 3 x + 9 y + 24 = 0

Rewrite

2 x^{2} + 4 x^{2} - 3 x + 9 y + 24 = 0

in the standard form

4 (- \frac{3}{8}) (y - (- \frac{21}{8})) = (x - \frac{1}{4})^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{4}, - \frac{21}{8}), p = - \frac{3}{8}

(y - 5)^{2} + 4 x \geq - 2

y^{2} + 4 x - 80 y + 20 = 0

x^{2} - 5 x + 6 k (x) = 0

3 x^{2} - 12 x + k (x) > 0

x + 3 x - 5 = \frac{1}{3} y^{2}

What is 2x^2+4x^2-3x+9y+24=0 ?
The solution to 2x^2+4x^2-3x+9y+24=0 is Parabola with (h,k)=(1/4 ,-21/8),p=-3/8