What is 4x^2+4y+4x-12y-10=0 ?

The solution to 4x^2+4y+4x-12y-10=0 is Parabola with (h,k)=(-1/2 ,-11/8),p= 1/2

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4x^2+4y+4x-12y-10=0

4 x^{2} + 4 y + 4 x - 12 y - 10 = 0

(h, k) = (- \frac{1}{2}, - \frac{11}{8}), p = \frac{1}{2}

Solution steps

4 x^{2} + 4 y + 4 x - 12 y - 10 = 0

Rewrite

4 x^{2} + 4 y + 4 x - 12 y - 10 = 0

in the standard form

4 \cdot \frac{1}{2} (y - (- \frac{11}{8})) = (x - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{1}{2}, - \frac{11}{8}), p = \frac{1}{2}

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

(y - 4)^{2} = 20 (x - 1)

x - 1 y^{2} - 1 y - 1 = 0

2 y = x^{2} - 6 x + 9

y = x^{2} + 10 x - 171

What is 4x^2+4y+4x-12y-10=0 ?
The solution to 4x^2+4y+4x-12y-10=0 is Parabola with (h,k)=(-1/2 ,-11/8),p= 1/2