Question

If the distance of the point P(x,y) from A(a,0) be (a+x) then prove that y^2=4ax

Answer 1

The distance between 2 points P(x1,y1) and Q(x2,y2) is given by
sqrt( (x2-x1)^2 + (y2-y1)^2 )

So the distance here is
sqrt( (a-x)^2 + (0-y)^2 )
which is equal to (a +x)

So
(a-x)^2 +y^2 = (a+x)^2, squaring both the sides..
x^2 - 2ax + a^2 + y^2 = x^2 + 2ax + a^2
which implies
y^2 = 2ax + 2ax, 'cancelling' x^2 and y^2 and 'shifting' 2ax to right side.
or y^2 = 4ax...