1. ## parametrics locus halp

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!!

2. ## Re: parametrics locus halp

Originally Posted by sssona09
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.

3. ## Re: parametrics locus halp

Originally Posted by same1111
y=x^3+3 isnt a parabola btw. I also got a different answer for 3 so maybe the question is wrong.
y=x^2 +3 for q3 oops

wait can u post ur working out please?

5. ## Re: parametrics locus halp

Originally Posted by same1111
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.. ?

6. ## Re: parametrics locus halp

Originally Posted by sssona09
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.

7. ## Re: parametrics locus halp

Originally Posted by same1111
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!!! MUCH LUb

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•