Find all points on the XY plane where

nomadzkia0re

nomadzkia0re

Answered question

2022-04-03

Find all points on the XY plane where parabola y=x24px+2p23 doesn't pass. Note that PR.

Answer & Explanation

Jermaine Lam

Jermaine Lam

Beginner2022-04-04Added 11 answers

 f(x)=x24px+2p23
Suppose (a,b) is a point the parabola cannot pass through for any value of p. We want to find the locus of this point. Consider the equation
f(a)=b

a24pa+2p23=b

2p24pa+a2b3=0
The condition is that this quadratic in p should have no solution, i.e. for any value of b there should be no value of a such that this equation holds for any p.
D<0

16a28(a2b3)<0

b<a23
I believe the answer you gave has a typo.

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