parametrics locus halp (1 Viewer)

sssona09

Member
Joined
Oct 2, 2015
Messages
90
Gender
Female
HSC
2018
pls help :(
2. The tangent at a point P(2ap,ap^2) on the parabola x^2=4ay meets the x-axis at A and the y-axis at B. Find and describe the locus of the midpoint M of AB.

3. Consider the parabola x^2=4ay. If the normal at P(2p,p^2) and Q(2q,q^2) intersect at right angles at R, show that the locus of R is the parabola y=x^3+3

I tried but my answer for 3 was invalid :/

thank you all!!
 

same1111

Member
Joined
Feb 16, 2017
Messages
46
Gender
Undisclosed
HSC
N/A
pls help :(
2. The tangent at a point P(2ap,ap^2) on the parabola x^2=4ay meets the x-axis at A and the y-axis at B. Find and describe the locus of the midpoint M of AB.

3. Consider the parabola x^2=4ay. If the normal at P(2p,p^2) and Q(2q,q^2) intersect at right angles at R, show that the locus of R is the parabola y=x^3+3

I tried but my answer for 3 was invalid :/

thank you all!!
y=x^3+3 isnt a parabola btw. I also got a different answer for 3 so maybe the question is wrong.
 

same1111

Member
Joined
Feb 16, 2017
Messages
46
Gender
Undisclosed
HSC
N/A
wait how is the y coordinate of R (the first line of working) a(p^2+q^2+pq+2)

like where is the 2 from

I thought its not there.. ?
its the intersection of the normals.. If you solve the two equations for the normal of q and p you get that for the y coordinate.
 

sssona09

Member
Joined
Oct 2, 2015
Messages
90
Gender
Female
HSC
2018
its the intersection of the normals.. If you solve the two equations for the normal of q and p you get that for the y coordinate.
ohh!! lol
thank YOU SO MUCH FOR THE WORKING OUT!!! :D MUCH LUb
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top