ANSWER
[tex]x = - 6[/tex]
EXPLANATION
The given parabola has equation:
[tex] {(y - 3)}^{2} = 20 {(x + 1)}^{2} [/tex]
This parabola opens in the direction of the positive x-axis.
This can be rewritten as:
[tex]{(y - 3)}^{2} = 4(5) {(x + 1)}^{2} [/tex]
The vertex is (-1,3)
The directrix of this parabola is
[tex]x = - 1 - 5[/tex]
[tex]x = - 6[/tex]
Answer:
The equation of the directrix of the parabola is x=-6.
Step-by-step explanation:
The given equation is
[tex](y-3)^2=20(x+1)[/tex] .... (1)
If a parabola is defined as
[tex](y-k)^2=4p(x-h)[/tex] .... (2)
Where, (h,k) is vertex and the directix of the parabola is x=h-p.
From (1) and (2), we get
[tex]h=-1,k=3[/tex]
[tex]4p=20[/tex]
[tex]p=5[/tex]
The value of p is 5.
The equation of directix is
[tex]x=h-p[/tex]
[tex]x=-1-5[/tex]
[tex]x=-6[/tex]
Therefore the equation of the directrix of the parabola is x=-6.
