What is the standard form of the equation of the parabola with a directrix at x=-2 and a focus at (-3,3)?

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Answer 1 · 2016-08-21T18:38:08

# (y-3)^2=-(2x+5)#, is the reqd. eqn. of Parabola.

Let #F(-3,3)# be the Focus, and, # d : x+2=0# the Directrix of the

reqd. Parabola denoted by #S#.

It is known from the Geometry, that, if #P(x,y) in S#, then, the #bot#-

distance btwn. the pt. #P# & #d# is the same as the distance btwn.

the pts. #F# & #P#.

This Property of Parabola is known as the Focus Directrix Property

of Parabola.

#:. |x+2|=sqrt{(x+3)^2+(y-3)^2}#

#:. (y-3)^2+(x+3)^2-(x+2)^2=0#

#:. (y-3)^2=-(2x+5)#, is the reqd. eqn. of Parabola.