Prove that the equation to the parabola, whose vertex and focus are on the axis of x at distances a and a′ from the origin respectively, is y2=4(a′−a)(x−a).
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Solution
The general equation of parabola is (y−k)2=4A(x−h) where (h,k) is the vertex of of the parabola
A is the distance between the vertex and the focus, so in our case