Question

write the equation of the directrix of the parabola shown below. Write your answer without using spaces. y^2 - 4x + 4y - 4= 0

Answer 1

Answer: x = -3

Step-by-step explanation: .....

Answer 2

y = - 3

Explanation:

The general form of the equation of a parabola is given by:

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

with foci (h,k) and directrix equation given by y = k - p.

The parabola equation that you have is

`y^2-4x+4y-4=0`

you complete squares to get the general form of the equation:

`(y^2+4y+4)-4-4=4x\\\\(y+2)^2=4x+8\\\\(y+2)^2=4(x-(-(8)/(4)))\\\\(y+2)^2=4(1)(x-(-2))`

`(y-(-2))^2=4(1)(x-(-2))`

Next, you compare the last expression with the general for of the equation of a parabola and you obtain:

`k = -2\\\\h=-2\\\\p=1`

hence, the directrix equation is y = k - p = - 2 - 1 = - 3