The vertex is 3 units from the focus, and the parabola opens to the right, so the equation is of the form y^2 = 4px:
(y-4)^2 = 6(x-2)^2
What is the equation of the parabola with vertex (2, 4) and focus (5, 4)?
2 answers
This equation can also be written as:
4p(x - h) = (y - k)^2
Where (h, k) is the vertex. Substituting the given values of the vertex and focus, we get:
4p(x - 2) = (y - 4)^2
and
p = 3/4
Substituting this value of p in the first equation, we get:
(y - 4)^2 = 6(x - 2)
Expanding and simplifying, we get:
y^2 - 8y + 16 = 6x - 12
or
y^2 - 8y - 6x + 28 = 0
Therefore, the equation of the parabola is:
y^2 - 8y - 6x + 28 = 0.
4p(x - h) = (y - k)^2
Where (h, k) is the vertex. Substituting the given values of the vertex and focus, we get:
4p(x - 2) = (y - 4)^2
and
p = 3/4
Substituting this value of p in the first equation, we get:
(y - 4)^2 = 6(x - 2)
Expanding and simplifying, we get:
y^2 - 8y + 16 = 6x - 12
or
y^2 - 8y - 6x + 28 = 0
Therefore, the equation of the parabola is:
y^2 - 8y - 6x + 28 = 0.
0 answers