Question 968922

the standard form equation of a parabola with directrix {{{x=-2}}} and focus ({{{2}}},{{{0}}}):

Let p({{{x}}},{{{ y}}}) ba any point on the parabola.

By definition of parabola,p({{{x}}},{{{ y}}}) is {{{equidistant}}} from the focus and the directirx. Thus, we have

{{{(x-2)^2 + (y-0)^2 = (x-(-2))^2}}}

 {{{(y-0)^2 = (x+2)^2-(x-2)^2}}} 

 {{{y^2 = (x^2+4x+4)-(x^2-4x+4)}}}

 {{{y^2 = x^2+4x+4-x^2+4x-4}}}

{{{y^2 = cross(x^2)+4x+cross(4)-cross(x^2)+4x-cross(4)}}}

{{{y^2 = 4x+4x}}}

{{{y^2 = 8x}}}=> your answer


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,0,.12),locate(2,-0.5,F(2,0)),line(-2,10,-2,-10),
 graph( 600, 600, -10, 10, -10, 10,-sqrt(8x) ,sqrt(8x))) }}}