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Which is the equation of the parabola with focus (6, 2) and vertex (6, –4)?

Sagot :

Lanuel

Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).

How to determine the equation of this parabola?

Mathematically, the standard equation with the vertex for a parabola is given by:

(y - k)² = 4a(x - h) for horizontal parabola.

(x - h)² = 4a(y - k) for vertical parabola.

where:

  • h and k are the vertex.
  • a is a point.

By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.

Given the following data:

Focus with points = (6, 2).

Vertex (h, k) = (6, –4).

Note: a = 2 - (-4) = 2 + 4 = 6.

Substituting the given parameters into the formula, we have;

(x - 6)² = 4 × 4(y - (-4))

(x - 6)² = 16(y + 4).

Read more on parabola here: https://brainly.com/question/2346582

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