Question

The equation of a parabola is (y−3)2=20(x+1) .

Answer 1

Answer:

The equation of the directrix of the parabola is x=-6.

Step-by-step explanation:

The given equation is

$(y-3)^2=20(x+1)$            .... (1)

If a parabola is defined as

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

Where, (h,k) is vertex and the directix of the parabola is x=h-p.

From (1) and (2), we get

$h=-1,k=3$

$4p=20$

$p=5$

The value of p is 5.

The equation of directix is

$x=h-p$

$x=-1-5$

$x=-6$

Therefore the equation of the directrix of the parabola is x=-6.

Answer 2

ANSWER

$x = - 6$

EXPLANATION

The given parabola has equation:

${(y - 3)}^{2} = 20 {(x + 1)}^{2}$

This parabola opens in the direction of the positive x-axis.

This can be rewritten as:

${(y - 3)}^{2} = 4(5) {(x + 1)}^{2}$

The vertex is (-1,3)

The directrix of this parabola is

$x = - 1 - 5$

$x = - 6$