Advance Math Help!! (1 Viewer)

[viraj30]

show that for points 'p' and 'q' on the parabola x= 2at, y=at^2 the tangents meet at (a(p+q), apq)

Also, i get confused with letters x, y, p, q, t..are they variables or constants?? god i am lost!!!

help would be much appreciated!

 

[nightweaver066]

This is 3U mathematics topic under Parametric Equations.

Let P = (2ap, ap^2), Q = (2aq, aq^2) where p and q are parameters which are constants.

Keep in mind that you are looking for a point of intersection between two tangents. This means you are required to find an x and a y value.




Therefore



At P(2ap, ap^2), dy/dx = p
Equation of tangent at P:




Similarly,
Equation of tangent at Q:


Solving (1) and (2) for intercepts,




From (1),



Therefore the tangents at P and Q meet at (a(p+q), apq)

 

[barbernator]

what do you use to get that form of script nightweaver?

 

[D94]

what do you use to get that form of script nightweaver?

Latex. http://community.boredofstudies.org/showthread.php?t=234262 Or you can click the fx button just above where you make your reply/post.

 

[barbernator]

brilliant good luck in 4u on monday and 3u on wednesday

 

[viraj30]

This is 3U mathematics topic under Parametric Equations.

Let P = (2ap, ap^2), Q = (2aq, aq^2) where p and q are parameters which are constants.

Keep in mind that you are looking for a point of intersection between two tangents. This means you are required to find an x and a y value.




Therefore



At P(2ap, ap^2), dy/dx = p
Equation of tangent at P:




Similarly,
Equation of tangent at Q:


Solving (1) and (2) for intercepts,




From (1),



Therefore the tangents at P and Q meet at (a(p+q), apq)

can you tell what was the point of y= x^2/4a and differentiating it??

 

[nightweaver066]

can you tell what was the point of y= x^2/4a and differentiating it??

In order to find the gradient at that point. Once you have the gradient at that point, you can apply the point-gradient formula in order to obtain the equation of the tangent.