Question

the pointbon the parabola y square =4ax 3 nearest to the focus has its abscissa

Answer 1

Let P(x, y) is the point on the parabola in such a way that distance between focus and it is minimum or this point is nearest to the focus.

given equation of parabola is y² = 4ax
Focus of parabola is (a , 0)
now, distance between (x , y) and (a,0)
S = $\sqrt{(x-a)^2 + (y-0)^2}$
S = $\sqrt{(x-a)^2 + y^2}$
Because point lies on the parabola so, y² = 4ax , put it above
S = $\sqrt{(x-a)^2 + 4ax}$
= $\sqrt{(x + a)^2}$ = |x + a |
Now, S will be minimum when x = 0

Hence, Abscissa , x = 0 is the answer