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liraira [26]
3 years ago
13

Px + qy = r 2px - qy = 2r When solving this system of equations, x =

Mathematics
2 answers:
VladimirAG [237]3 years ago
8 0
Px + qy = r
2px - qy = 2r
----------------add
3px = 3r

x = 3r/3p
x = r/p
expeople1 [14]3 years ago
8 0
You just add the equations:
  px + qy = r
2px  - qy = 2r
3px = 3r
divide by 3
px = r
divide by p
x = (r)/(p)
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\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=7\\ p=-2 \end{cases}\implies 4(-2)[x-(-5)]=[y-7]^2 \\\\\\ -8(x+5)=(y-7)^2\implies x+5=\cfrac{(y-7)^2}{-8}\implies \boxed{x=-\cfrac{1}{8}(y-7)^2-5}

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