Respuesta :
The equation that represents a parabola is x^2 = 12(y-2).
What is a parabola?
Parabola is a open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is the locus of a point that is equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix.
For the given situation,
A parabola with a focus of (h,k+p) is (0, 5) and
A directrix of y = (k-p) = -1
Here,
[tex]k+p=5\\k-p=-1[/tex]
On solving these equations,
[tex]k=2, p =3[/tex]
The general equation of parabola is
[tex](x-h)^{2} =4p(y-k)[/tex]
On substituting all the values,
⇒ [tex](x-0)^{2} =4(3)(y-2)[/tex]
⇒ [tex]x^{2} =12(y-2)[/tex]
Hence we can conclude that the equation that represents a parabola is x^2 = 12(y-2).
Learn more about parabola here
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