The coordinate of the vertex of the parabola is option (C) (1,-2) is the correct answer.
What is the equation of the parabola?
The set of all points in a plane that are equidistant from a fixed line and a fixed point (not on the fixed line) in the plane is a parabola. The fixed line is the ‘directrix’ and the fixed point is the ‘focus’. The point of intersection of the parabola with the axis is the vertex.
For the given situation,
The equation of parabola is [tex](x-1)^2=12(y+2)[/tex] ------ (1)
The diagram below shows the parabola and the vertex of the equation of parabola.
The general form of the equation of parabola is
[tex](x-h)^{2} =4a(y-k)[/tex]
Here the vertex is (h,k)
Now compare the equation 1 with this general form, we get
⇒ [tex]h=1[/tex] and [tex]k=-2[/tex]
Hence we can conclude that the coordinate of the vertex of the parabola is option (C) (1,-2) is the correct answer.
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