The focus of a parabola is (-10, -7), and its directrix is x = 16. Fill in the missing terms and signs in the parabola's equation in standard form. (y )^2= (x )
Accepted Solution
A:
ANSWER
[tex](y + 7)^2= - 52(x-3)[/tex]
It was given that the parabola has its focus at:
(-10,-7)
and directrix at:
x=16.
We need to determine the vertex of this parabola which is midway between the focus and the directrix.
Therefore the vertex will be at,
[tex]( \frac{16 + - 10}{2} , - 7)[/tex]
[tex](3, - 7)[/tex]
The equation of this parabola is of the form:
[tex](y-k)^2=4p(x-h)[/tex]
where p is the distance from the vertex to the focus.
[tex] |p| = 16 - 3 = 13[/tex]
Since the parabola opens towards the negative direction of the x-axis,
[tex]p = - 13[/tex]
We substitute the vertex and the value for p to get;