Hocus Focus
Geometry
Level
pending
What is the focal length of the parabola written in the form:
a + b
b + c
c
b - c
c - b
b
1
a
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1 solution
Expand the expressions:
Cancel like terms:
Combine like terms:
Factor out 4c:
The last equation is the equation of the parabola where (a, b) is the vertex and c is the focal length.
And also, the original equation is based on the definition of a parabola. The left side is the square of the distance from a point (x, y) to the focus (a, b + c) and the right is the distance from the same point to the directrix y = b - c .