Locus: Help please (1 Viewer)

[Jkitty]

3. Find the point of intersection between the
i. tangent
Ii. Normal to the curve
A. x^2=4y at the points (2p,p^2) and 2q,q^2)


Thank you

 

[braintic]

That is just bookwork. It should be in your notes. Or look in the textbook.

 

[Jaguar33]

need help with the same question

 

[Jkitty]

That is just bookwork. It should be in your notes. Or look in the textbook.

It does not show any examples on this type of question.... unfortunately....

 

[Jaguar33]

i found out how to do it! Right, so first for i) tangent,

1. You differentiate x^2=4y, which will give you a gradient of p.
2. Use the equation formula (y-y1)=m(x-x1)
and place the first points in (2p, p^2)
this will give you an equation of y=px - p^2

Then do this step again, except with the other points (2q,q^2)
and you will get y=qx-q^2

Make the two equations you have found, and make them equal each other. Then proceed, to put any terms with x on the left side, and the other on p side,
Then factorise
So it will look like this by now
x(p-q) = p(p-q)(p+q)
cross out, then you have the first point of intersection for x= p +q. Then sub this back in to get why

and i havent done the 2nd part, but im guessing u do the same for the normal

 

[Jkitty]

i found out how to do it! Right, so first for i) tangent,

1. You differentiate x^2=4y, which will give you a gradient of p.
2. Use the equation formula (y-y1)=m(x-x1)
and place the first points in (2p, p^2)
this will give you an equation of y=px - p^2

Then do this step again, except with the other points (2q,q^2)
and you will get y=qx-q^2

Make the two equations you have found, and make them equal each other. Then proceed, to put any terms with x on the left side, and the other on p side,
Then factorise
So it will look like this by now
x(p-q) = p(p-q)(p+q)
cross out, then you have the first point of intersection for x= p +q. Then sub this back in to get why

and i havent done the 2nd part, but im guessing u do the same for the normal

Thank you so much

 

[braintic]

You should be asking your teacher why they haven't given you an example of this in class.