The equation (y + 1)² = -12(x - 2) represents the given parabola.
What is a parabola?
A parabola is a U-shaped plane curve. It is assumed to be mirror symmetrical. A parabola is produced by the intersection of a right circular cone and a plane parallel to the cone.
The vertex is at (-2, 1) and the directrix is x = 5.
Therefore, the vertex of the given parabola is at 2nd quadrant.
Again, the directrix is also parallel to the y-axis.
As a result, the parabola will open towards the left.
The general form of a parabola is (y - k)² = 4a(x - h)
Here, h and k are x and y coordinates respectively of the vertex.
Now, the coordinates of the focus are (h + a , k) and the directrix is at x = h − a.
Therefore, h - a = 5 (as, x =5)
⇒ 2 - a = 5
⇒ a = -3
Therefore, the equation of the parabola is (y − k)² = 4a(x − h)
⇒ [y - (-1)]² = 4(- 3)(x - 2)
⇒ (y + 1)² = -12(x - 2)
The equation of the parabola that has a vertex (2 , -1) and a directrix
of x = 5 is (y + 1)² = -12(x - 2)
Learn more about parabola here: https://brainly.com/question/4074088
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