What is the standard form of the parabola with a vertex at (16,5) and a focus at (16,-17)?

1 Answer
Jim G.
Feb 4, 2018

#(x-16)^2=-88(y-5)#

Explanation:

#"since the vertex is known use the vertex form of "#
#"the parabola"#

#•color(white)(x)(y-k)^2=4a(x-h)" for horizontal parabola"#

#•color(white)(x)(x-h)^2=4a(y-k)" for vertical parabola"#

#"where a is the distance between the vertex and the focus"#

#"and "(h,k)" are the coordinates of the vertex"#

#"since the x-coordinates of the vertex and focus are 16"#
#"then this is a vertical parabola "uuu#

#rArr(x-16)^2=4a(y-5)#

#rArra=-17-5=-22#

#rArr(x-16)^2=-88(y-5)#

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