Locus question !!! (1 Viewer)

[ssukarieh1]

Ok so i managed to answer this question, however i could not manage to prove that the locus of N is a normal to the parabola. Any ideas?? Thanks, all help is much appreciated!!

View attachment 31678

 

[Squar3root]

 

[ssukarieh1]

hahahhaahahahahhahahah

 

[FrankXie]

Since you have managed to work out all other parts, I believe you have had a quite good understanding of the question. So I only give you a few hints and don't need to waste time posting the full solution.
1. Find the equation of the locus as required by the question ( I think you have obtained it? good )
2. If indeed this line ( the locus) is a normal, at which point must this normal be? i.e., find x0, so that at x=x0, the gradient of normal equals to the gradient of this line ( the locus)
3. Then find y0=x0^2/4a, and use point-gradient formula to write the normal at the point (x0,y0)
4. Does the normal coincide with the equation of the locus? Yes? good, u got it.

 

[ssukarieh1]

Yessss I understand Thankyou for ur wonderful explanation! It is much appreciated!