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Thread: parametrics locus halp

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    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!!

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    Re: parametrics locus halp

    Quote Originally Posted by sssona09 View Post
    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.

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    Re: parametrics locus halp

    Quote Originally Posted by same1111 View Post
    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?

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    Re: parametrics locus halp


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    Re: parametrics locus halp

    Quote Originally Posted by same1111 View Post
    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.. ?

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    Re: parametrics locus halp

    Quote Originally Posted by sssona09 View Post
    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.

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    Re: parametrics locus halp

    Quote Originally Posted by same1111 View Post
    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

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