What is x^2-10x-15y+21=0 ?

The solution to x^2-10x-15y+21=0 is Parabola with (h,k)=(5,-4/15),p= 15/4

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x^2-10x-15y+21=0

x^{2} - 10 x - 15 y + 21 = 0

(h, k) = (5, - \frac{4}{15}), p = \frac{15}{4}

Solution steps

x^{2} - 10 x - 15 y + 21 = 0

Rewrite

x^{2} - 10 x - 15 y + 21 = 0

in the standard form

4 \cdot \frac{15}{4} (y - (- \frac{4}{15})) = (x - 5)^{2}

Therefore parabola properties are:

(h, k) = (5, - \frac{4}{15}), p = \frac{15}{4}

y - 5 = - 2 (x + 1)^{2}

y - x^{2} \geq 0

(y - (15))^{2} = 2 (x - 1)

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

(y - 1)^{2} = 4 (x - 3)

What is x^2-10x-15y+21=0 ?
The solution to x^2-10x-15y+21=0 is Parabola with (h,k)=(5,-4/15),p= 15/4