The equation of the parabola is:
(y - 6)² = -12(x +2)
Parabola is the locus of a point such that its distance from a fixed point (called the focus) and a given line (called the directrix) is always the same.
The equation of a parabola is given by:
(y - k)² = 4p(x - h)
Where (h, k) is the vertex, (h + p, k) is the focus
Given the vertex of a parabola is (-2,6), and its focus is (-5,6).
Hence, k = 6, h = -2;
h + p = -5
-2 + p = -5
p = -3
Hence the equation of the parabola is:
(y - 6)² = -12(x +2)
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