Derive the equation of the parabola with a focus at (2, - 1) and a directrix of y = - one half.

f (x) = - (x + 2) 2 - three fourths

f (x) = (x + 2) 2 + three fourths

f (x) = - (x - 2) 2 + three fourths

f (x) = - (x - 2) 2 - three fourths

Question

Mathematics

Lainey

26 December, 18:32

Derive the equation of the parabola with a focus at (2, - 1) and a directrix of y = - one half.

f (x) = - (x + 2) 2 - three fourths

f (x) = (x + 2) 2 + three fourths

f (x) = - (x - 2) 2 + three fourths

f (x) = - (x - 2) 2 - three fourths

+2

Answers (1)

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Mario Lutz · Answer 1

From the given data, the parabola should be opening downward. The length from the vertex to the focus is equal to the length from the vertex to the directrix. In this case, the vertex of the parabola should be at y = - 3/4 and x = 2. Hence, the equation becomes C. f (x) = - (x - 2) 2 + three fourths

Derive the equation of the parabola with a focus at (2, - 1) and a directrix of y = - one half.f (x) = - (x + 2) 2 - three fourthsf (x) = (x + 2) 2 + three fourthsf (x) = - (x - 2) 2 + three fourthsf (x) = - (x - 2) 2 - three fourths

Derive the equation of the parabola with a focus at (2, - 1) and a directrix of y = - one half.

f (x) = - (x + 2) 2 - three fourths

f (x) = (x + 2) 2 + three fourths

f (x) = - (x - 2) 2 + three fourths

f (x) = - (x - 2) 2 - three fourths