What is q^1=105-3p^1+p^2 ?

The solution to q^1=105-3p^1+p^2 is Parabola with (h,k)=(411/4 , 3/2),p= 1/4

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q^1=105-3p^1+p^2

q^{1} = 105 - 3 p^{1} + p^{2}

(h, k) = (\frac{411}{4}, \frac{3}{2}), p = \frac{1}{4}

Solution steps

q^{1} = 105 - 3 p^{1} + p^{2}

Rewrite

q^{1} = 105 - 3 p^{1} + p^{2}

in the standard form

4 \cdot \frac{1}{4} (q - \frac{411}{4}) = (p - \frac{3}{2})^{2}

Therefore parabola properties are:

(h, k) = (\frac{411}{4}, \frac{3}{2}), p = \frac{1}{4}

x^{2} = 50 y

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

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

9 y = x^{2}

d x = \frac{6 y}{x}

What is q^1=105-3p^1+p^2 ?
The solution to q^1=105-3p^1+p^2 is Parabola with (h,k)=(411/4 , 3/2),p= 1/4