Question

Which expression represents the equation of the parabola with focus of (-3,3) and directrix y

Answer 1

Equation of the parabola with focus of (-3,3) and directrix y

`(x+3)^(2)=4a(y+a-3)`

Explanation:

As directix is not give so writing it in form of a.

Standard equation for parabola with directix is y = k - a and focus (h,k+a)

`(x-h)^(2)=4a(y-k)---(1)`

Given that focus is (-3, 3)

(-3, 3) = (h, k +a)

by comparison

h= -3

k+a = 3

a = 3 - a

Substituting this value in (1)

`(x-(-3))^(2)=4a(y-(3-a))\\(x+3)^(2)=4a(y+a-3)\\`