What is (3y^{(2)}-30y+2x+(101))/((2))=0 ?

The solution to (3y^{(2)}-30y+2x+(101))/((2))=0 is Parabola with (h,k)=(-13,5),p=-1/6

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(3y^{(2)}-30y+2x+(101))/((2))=0

\frac{3 y ^{(2)} - 30 y + 2 x + ( 101 )}{( 2 )} = 0

(h, k) = (- 13, 5), p = - \frac{1}{6}

Solution steps

\frac{3 y ^{2} - 30 y + 2 x + 101}{2} = 0

Rewrite

\frac{3 y ^{2} - 30 y + 2 x + 101}{2} = 0

in the standard form

4 (- \frac{1}{6}) (x - (- 13)) = (y - 5)^{2}

Therefore parabola properties are:

(h, k) = (- 13, 5), p = - \frac{1}{6}

(y + 2)^{2} = 20 (x - 3)

(x + 3)^{2} = 12 (y + 5)

y - 5 x^{2} = 2 x - 6

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

x^{2} + x + h (x) - \frac{15 h ( x )}{4} = 0

What is (3y^{(2)}-30y+2x+(101))/((2))=0 ?
The solution to (3y^{(2)}-30y+2x+(101))/((2))=0 is Parabola with (h,k)=(-13,5),p=-1/6