Answer:
C. [tex]x = 3\cdot (y-3)^{2}+1[/tex]
Step-by-step explanation:
From Analytical Geometry, the equation of a parabola with axis of symmetry parallel to the x-axis and centered in [tex]V(x,y) = (h,k)[/tex] is described below:
[tex]x-h = C\cdot (y-k)^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex.
[tex]C[/tex] - Vertex factor.
If we know that [tex]h = 1[/tex] and [tex]k = 3[/tex], then the equation of the parabola is:
[tex]x-1 = C\cdot (y-3)^{2}[/tex]
[tex]x = C\cdot (y-3)^{2}+1[/tex]
Therefore, the option that could be its equation is C.
