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What is an equation of a parabola with the given vertex and focus?
vertex: (–2,5)
; focus: (–2,6)
Since the vertex is (-2,5), we know that the equation of the parabola will take the form:
(x + 2)^2 = 4p(y - 5)
where p is the distance between the vertex and the focus.
The distance between the vertex and the focus is 1 unit vertically upwards, so p = 1.
Therefore, the equation of the parabola is:
(x + 2)^2 = 4(y - 5)
Which can also be written in standard form as:
y = 1/4(x + 2)^2 + 5