Answer:
The equation of parabola is given by : ![(x-4) = \frac{-1}{3}(y+3)^{2}](https://tex.z-dn.net/?f=%28x-4%29%20%3D%20%5Cfrac%7B-1%7D%7B3%7D%28y%2B3%29%5E%7B2%7D)
Step-by-step explanation:
Given that vertex and focus of parabola are
Vertex: (4,-3)
Focus:(
,-3)
The general equation of parabola is given by.
, When x-componet of focus and Vertex is same
, When y-componet of focus and Vertex is same
where Vertex: (h,k)
and p is distance between vertex and focus
The distance between two points is given by :
L=![\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28X2-X1%29%5E%7B2%7D%2B%28Y2-Y1%29%5E%7B2%7D%7D)
For value of p:
p=![\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28X2-X1%29%5E%7B2%7D%2B%28Y2-Y1%29%5E%7B2%7D%7D)
p=![\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%284-%5Cfrac%7B47%7D%7B12%7D%29%5E%7B2%7D%2B%28%28-3%29-%28-3%29%29%5E%7B2%7D%7D)
p=![\sqrt{(\frac{1}{12})^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%5Cfrac%7B1%7D%7B12%7D%29%5E%7B2%7D%7D)
p=
and p=![\frac{-1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B12%7D)
Since, Focus is left side of the vertex,
p=
is required value
Replacing value in general equation of parabola,
Vertex: (h,k)=(4,-3)
p=
![(x-h) = 4p(y-k)^{2}](https://tex.z-dn.net/?f=%28x-h%29%20%3D%204p%28y-k%29%5E%7B2%7D)
![(x-4) = 4(\frac{-1}{12})(y+3)^{2}](https://tex.z-dn.net/?f=%28x-4%29%20%3D%204%28%5Cfrac%7B-1%7D%7B12%7D%29%28y%2B3%29%5E%7B2%7D)
![(x-4) = \frac{-1}{3}(y+3)^{2}](https://tex.z-dn.net/?f=%28x-4%29%20%3D%20%5Cfrac%7B-1%7D%7B3%7D%28y%2B3%29%5E%7B2%7D)
G^5 -g = g(g^4 -1)=g(g^2 -1)(g^2 +1) = g(g-1)(g+1)(g^2 +1)
24g^2 -6g^4 = 6g^2(4 -g^2) = 6g^2(2 -g)(2 +g)
Answer:
12% is the answer for this question