What is the equation of the parabola that has a vertex at # (-4, 2) # and passes through point # (-12,-3) #?

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Answer 1 · 2018-07-02T22:37:13

#(y-2)^2=-25/8(x+4)#

OR

#(x+4)^2=-64/5(y-2)#

Case 1: Horizontal parabola

Let the equation of horizontal parabola with the vertex #(x_1, y_1)\equiv(-4, 2)# be as follows

#(y-y_1)^2=4a(x-x_1)#

#(y-2)^2=4a(x+4)#

Since above parabola passes through the point #(-12, -3)# hence it will satisfies above equation as follows

#(-3-2)^2=4a(-12+4)#

#a=-25/32#

hence, the equation of horizontal parabola

#(y-2)^2=4(-25/32)(x+4)#

#(y-2)^2=-25/8(x+4)#

Case 2: Vertical parabola

Let the equation of vertical parabola with the vertex #(x_1, y_1)\equiv(-4, 2)# be as follows

#(x-x_1)^2=4a(y-y_1)#

#(x+4)^2=4a(y-2)#

Since above parabola passes through the point #(-12, -3)# hence it will satisfies above equation as follows

#(-12+4)^2=4a(-3-2)#

#a=-16/5#

hence, the equation of vertical parabola

#(x+4)^2=4(-16/5)(y-2)#

#(x+4)^2=-64/5(y-2)#