Parabola is the set of points at an equal distance from a fixed point ( focus ) and a fixed line (directrix)
Example of parabola in real life : ST louis arch in USA
A symmetrical open plane curve formed
by the intersection of a cone with a plane
parallel to its side
the standard form for a parabola with its directrix parallel to the x-axis is (x-h)^2 =4P ( y-k)
the standard form for a parabola with its directrix parallel to the y-axis is (y-k)^2 =4P ( x-h)
(h,k) is the coordinate of the vertex
P is the distance between the focus and the vertex as is the distance between the vertex and directrix
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the general form for a parabola with its directrix parallel to the x-axis is A(x^2) + Bx + Cy + D =0
the general form for a parabola with its directrix parallel to the y-axis isA (y^2) + By + Cx + D =0
-Example of a vertical parabola
Vertex ( 0.0 )
P is 2
Standard form is x^2 = 4 ( 2 ) Y
general conic form for this example is x^2 - 8 y = 0
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Vertex coordinate ( 1.2 )
P = 2
standard form is ( y-2 )^2 = 4 (2) (x-1)
general conic form for this example is : y^2 - 4y - 8x +12 = 0
