Answer:
The equation of parabola is given by : [tex](x-4) = \frac{-1}{3}(y+3)^{2}[/tex]
Step-by-step explanation:
Given that vertex and focus of parabola are
Vertex: (4,-3)
Focus:([tex]\frac{47}{12}[/tex],-3)
The general equation of parabola is given by.
[tex](x-h)^{2} = 4p(y-k)[/tex], When x-componet of focus and Vertex is same
[tex](x-h) = 4p(y-k)^{2}[/tex], 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=[tex]\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}[/tex]
For value of p:
p=[tex]\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}[/tex]
p=[tex]\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}[/tex]
p=[tex]\sqrt{(\frac{1}{12})^{2}}[/tex]
p=[tex]\frac{1}{12}[/tex] and p=[tex]\frac{-1}{12}[/tex]
Since, Focus is left side of the vertex,
p=[tex]\frac{-1}{12}[/tex] is required value
Replacing value in general equation of parabola,
Vertex: (h,k)=(4,-3)
p=[tex]\frac{-1}{12}[/tex]
[tex](x-h) = 4p(y-k)^{2}[/tex]
[tex](x-4) = 4(\frac{-1}{12})(y+3)^{2}[/tex]
[tex](x-4) = \frac{-1}{3}(y+3)^{2}[/tex]
