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The directrix and focus of a parabola are shown on the graph. Which is an equation for the parabola?

A. y= 12(x+2)^2-3
B. x= -1/12(y-3)^2-2
C. y= -12(x+2)^2-3
D. x= 1/12(y-3)^2-2

The directrix and focus of a parabola are shown on the graph Which is an equation for the parabola A y 12x223 B x 112y322 C y 12x223 D x 112y322 class=

Respuesta :

The equation for the given parabola is; x = ¹/₁₂(y - 3)² - 2

How to find the equation of a parabola?

From the graph, we see that;

Focus = (1, 3)

Directrix; x = -5

General form of equation of a parabola is;

(y - k)² = 4p(x - h)

where;

focus is (h + p, k)

directrix is x = h - p

Thus;

(1, 3) = (h + p, k)

h + p = 1  -----(1)

k = 3

Similarly;

h - p = -5   -----(2)

Add eq 1 to eq 2 to get;

2h = -4

h = -2

-2 - p = -5

p = 3

Thus, equation of the parabola is;

(y - 3)² = 4(3)(x - (-2))

(y - 3)² = 12(x + 2)

divide both sides by 12 to get;

¹/₁₂(y - 3)² = x + 2

x = ¹/₁₂(y - 3)² - 2

Read more about Equation of Parabola at; https://brainly.com/question/4061870

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