What is the equation of the parabola that has a vertex at # (21, 11) # and passes through point # (23,-4) #?

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Answer 1 · 2018-06-14T13:44:31

#2(y-11)^2=225(x-21)# (Parabola opened rightwards,(i.e,)towards positive x direction)

The General equation of a parabola is #(y-k)^2=4a(x-h)#

(Parabola opened towards positive x-direction)

where

#a# is a arbitrary constant,

( #h,k#) is the vertex.

Here we have our vertex as ( #21,11#).

SUBSTITUTE the x and y coordinate values of the vertex in the equation above, we get.

#(y-11)^2=4a(x-21)#

In order to find the value of ' #a#' substitute the given point in the equation

then we get

#(-4-11)^2=4a(23-21)#
# =>(-15)^2=8a#

#=>a=225/8#

Substitute the value for ' #a#' In the above equation to have the equation of the required parabola.

#(y-11)^2=4*225/8(x-21)#
#=>2(y-11)^2=225(x-21)#

#color(blue)(NOTE):#

The general equation of a parabola "OPENED UPWARDS " will

results in a slightly different equation , And leads to a different

answer . Its general form will be

#(x-h)^2=4*a(y-k)#

where (h,k) is the vertex..,