What is 3^2+3y^2-2x+y-6=0 ?

The solution to 3^2+3y^2-2x+y-6=0 is Parabola with (h,k)=(35/24 ,-1/6),p= 1/6

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3^2+3y^2-2x+y-6=0

3^{2} + 3 y^{2} - 2 x + y - 6 = 0

(h, k) = (\frac{35}{24}, - \frac{1}{6}), p = \frac{1}{6}

Solution steps

3^{2} + 3 y^{2} - 2 x + y - 6 = 0

Rewrite

3^{2} + 3 y^{2} - 2 x + y - 6 = 0

in the standard form

4 \cdot \frac{1}{6} (x - \frac{35}{24}) = (y - (- \frac{1}{6}))^{2}

Therefore parabola properties are:

(h, k) = (\frac{35}{24}, - \frac{1}{6}), p = \frac{1}{6}

y^{2} - 4 x - 6 y + 13 = 0

x = y (y - 2)

y \leq x^{2}

- x^{2} - 4 x - 6 y + 17 = 0

(x + 1)^{2} = 16 y

What is 3^2+3y^2-2x+y-6=0 ?
The solution to 3^2+3y^2-2x+y-6=0 is Parabola with (h,k)=(35/24 ,-1/6),p= 1/6