What is -7x^2+12x+25y^2=-16x^2+5y(5y-3)+10 ?

The solution to -7x^2+12x+25y^2=-16x^2+5y(5y-3)+10 is Parabola with (h,k)=(-2/3 , 14/15),p=-5/12

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-7x^2+12x+25y^2=-16x^2+5y(5y-3)+10

- 7 x^{2} + 12 x + 25 y^{2} = - 16 x^{2} + 5 y (5 y - 3) + 10

(h, k) = (- \frac{2}{3}, \frac{14}{15}), p = - \frac{5}{12}

Solution steps

- 7 x^{2} + 12 x + 25 y^{2} = - 16 x^{2} + 5 y (5 y - 3) + 10

Rewrite

- 7 x^{2} + 12 x + 25 y^{2} = - 16 x^{2} + 5 y (5 y - 3) + 10

in the standard form

4 (- \frac{5}{12}) (y - \frac{14}{15}) = (x - (- \frac{2}{3}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{2}{3}, \frac{14}{15}), p = - \frac{5}{12}

x^{2} - 2 x - 8 y + 9 = 0

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

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

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

y - x^{2} = - 4

What is -7x^2+12x+25y^2=-16x^2+5y(5y-3)+10 ?
The solution to -7x^2+12x+25y^2=-16x^2+5y(5y-3)+10 is Parabola with (h,k)=(-2/3 , 14/15),p=-5/12