I have a parabola vertex (11,3)
p is not given, focus pt is not given.
I need to find the equation of the parabola. How would I do this w/o p value or focus pt?
you cant. Þhere are an infinite number of parabolas that have that vertex.
You are correct that without the value of p or the coordinates of the focus point, you can't determine the specific equation of the parabola. The reason is that both p (the distance between the vertex and the focus) and the focus point are essential in defining a parabola.
However, with the given vertex (11,3), you can still write the general equation of a parabola in vertex form. The vertex form of a parabola equation is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
In this case, the vertex form can be written as: y = a(x - 11)^2 + 3.
Since we don't have the values of a, p, or the focus point, the equation remains in general form with 'a' as an arbitrary constant: y = a(x - 11)^2 + 3.
To obtain a specific equation for a parabola, you would need additional information like the value of 'a', the distance p, or the coordinates of the focus point. Without this information, the equation cannot be determined uniquely.