Question

find the equation of the parabola whose focus is (-2,3) and directix is the line 2x+3y-4=0​

Answer 1

Answer:

(x - 2)^2 = -4y + 16

Step-by-step explanation:

he standard form is (x - h)^2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p

Thus in this case:

(h, k + p) = (2, 3)

h = 2, k + p = 3

Directrix is y = k - p:

k - p = 5

k + p = 3

2k = 8

k = 4

p = 3 - 4 = -1

therefore the vertex is at(2, 4) and p = -1, the equation is:

(x - 2)^2 = -4(y - 4)

it can also be written as:

(x - 2)^2 = -4y + 16

4y = -(x - 2)^2 + 16

y = -1/4(x - 2)^2 + 4 => vertex form