Question

Ecuacion de parabola con foco (-2,5) directriz en x=3

Answer 1

The required equation of the parabola is (y-5)² = 20(x+2)

Equation of a parabola

The standard equation of a parabola is expressed as;

(y-k)² = 4p(x-h)

where;

vertex = (h, k)

focus = (p+k, k)

directrix x = -p + h

Note that the directrix given will determine the type of the equation of a parabola

Given the following parameters

focus = (-2, 5) = (h, k)

x = -p + h

3 = p -2

p = 5

Substitute

(y-k)² = 4p(x-h)

(y-5)² = 4(5)(x-(-2))

(y-5)² = 20(x+2)

Hence the required equation of the parabola is (y-5)² = 20(x+2)

Learn more on equation of parabola here; brainly.com/question/4061870

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