Find the equation of a parabola, whose vertex is at #(-3,2)# and passes through #(4,7)#?

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Answer 1 · 2017-04-05T12:45:15

#5x^2+30x-49y+143=0# or #7y^2-25x-28y-47=0#

There could be two type of parabolas with vertex as #(-3,2)#

A #(y-2)=a(x+3)^2# If this passes through #(4,7)#, we have

#(7-2)=a(4+3)^2# i.e. #a=5/49# and equation of parabola is

#(y-2)=5/49(x+3)^2# i.e. #49y-98=5x^2+30x+45# or

#5x^2+30x-49y+143=0#

B #(x+3)=a(y-2)^2# If this passes through #(4,7)#, we have

#(4+3)=a(7-2)^2# i.e. #a=7/25# and equation of parabola is

#(x+3)=7/25(y-2)^2# i.e. #25x+75=7y^2-28y+28# or

#7y^2-25x-28y-47=0#

graph{(5x^2+30x-49y+143)(7y^2-25x-28y-47)=0 [-11, 9, -1.36, 8.64]}