The point (0, -9) is the focus of the parabola shown. What is the equation of the parabola?
Solution:
The function of the parabola is written as
(x - h)2 = 4p (y - k)
Where (h + p, k) is the coordinate of the focus
(h, k) is the vertex
p is the distance between the focus with the vertex
It is given that
Distance of focus and vertex = - 9 - 0 = - 9
So the equation is
(x - h)2 = 4p (y - k)
Substituting the values
(x - 0)2 = 4 (-9) (y - 0)
x2 = - 36y
y = -1/36 x2
Therefore, the equation of the parabola is y = -1/36 x2.
The point (0, -9) is the focus of the parabola shown. What is the equation of the parabola?
Summary:
The point (0, -9) is the focus of the parabola shown. The equation of the parabola is y = -1/36 x2.