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The question is an illustration of parabolas
The equation of the flight path is:[tex]\mathbf{y = -\frac{5}{1089}(x - 33)^2 + 5}[/tex]
The vertex is given as:
[tex]\mathbf{(h,k) = (33,5)}[/tex]
A point on the curve is given as:
[tex]\mathbf{(x,y) = (0,0)}[/tex]
The general equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
Substitute [tex]\mathbf{(h,k) = (33,5)}[/tex]
[tex]\mathbf{y = a(x - 33)^2 + 5}[/tex]
Substitute [tex]\mathbf{(x,y) = (0,0)}[/tex]
[tex]\mathbf{0 = a(0 - 33)^2 + 5}[/tex]
[tex]\mathbf{0 = a(-33)^2 + 5}[/tex]
[tex]\mathbf{0 = a \times 1089 + 5}[/tex]
Collect like terms
[tex]\mathbf{a \times 1089 = -5}[/tex]
Solve for a
[tex]\mathbf{a = -\frac{5}{1089}}[/tex]
Substitute [tex]\mathbf{a = -\frac{5}{1089}}[/tex] in [tex]\mathbf{y = a(x - 33)^2 + 5}[/tex]
[tex]\mathbf{y = -\frac{5}{1089}(x - 33)^2 + 5}[/tex]
Hence, the required equation is [tex]\mathbf{y = -\frac{5}{1089}(x - 33)^2 + 5}[/tex]
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