What is 1/3 x-2x+1/17 y^2+1/17 y=-35/17 ?

The solution to 1/3 x-2x+1/17 y^2+1/17 y=-35/17 is Parabola with (h,k)=(417/340 ,-1/2),p= 85/12

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1/3 x-2x+1/17 y^2+1/17 y=-35/17

\frac{1}{3} x - 2 x + \frac{1}{17} y^{2} + \frac{1}{17} y = - \frac{35}{17}

(h, k) = (\frac{417}{340}, - \frac{1}{2}), p = \frac{85}{12}

Solution steps

\frac{1}{3} x - 2 x + \frac{1}{17} y^{2} + \frac{1}{17} y = - \frac{35}{17}

Rewrite

\frac{1}{3} x - 2 x + \frac{1}{17} y^{2} + \frac{1}{17} y = - \frac{35}{17}

in the standard form

4 \cdot \frac{85}{12} (x - \frac{417}{340}) = (y - (- \frac{1}{2}))^{2}

Therefore parabola properties are:

(h, k) = (\frac{417}{340}, - \frac{1}{2}), p = \frac{85}{12}

(y - 2)^{2} = 16 (x - 2)

x^{2} - 12 x - 10 y + 36 = 0

(x - 1)^{2} = 8 (y - 2)

y^{2} - y - x = 3

h s = 2 πh + 2 π r^{2}

What is 1/3 x-2x+1/17 y^2+1/17 y=-35/17 ?
The solution to 1/3 x-2x+1/17 y^2+1/17 y=-35/17 is Parabola with (h,k)=(417/340 ,-1/2),p= 85/12