Here is a neat answer by CY aries.
Here he has dropped a normal from parabola to line but I am unable to understand why not from line to parabola.
Original OP is inactive. So please do not close this question
2026-04-11 10:30:01.1775903401
Doubt regarding distance between parabola and a line(coordinate geometry)
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It is easier to calculate the distance of given point from given line and that point can be in parametric form, but for calculating it other way around, you need to take point (t, t+1) on the line, draw a perpendicular to the line which passes through point (t, t+1) which would be x+y=2t+1, as you can see this will involve multiple lines depending on value of t and this has to satisfy the point on x=$y^2$ Which would make equation as $y^2 +y = 2t+1$ Solve for values of y and then you would have to calculate distance for each of them, which is nothing but simply complicating a very simple problem.