Parametrics question (1 Viewer)

[TeheeCat]

P and Q are the points with parameters p and q on the parabola x = at^2, y = 2at.

a) Show that the chord PQ is 2x - (p+q)y + 2apq = 0

b) If OP is perpendicular to OQ, show that the x-intercept of PQ is independent of p and q.


I need help with both, but I'm particularly confused with b. What does it mean by "independent of p and q"?

Even hints are enough for me!

Thank you!

 

[fan96]

We have the points and

a) The equation of a line joining two points may be found by calculating the gradient (i.e. rise/run) using the two points, and then using the point-gradient formula with either point.

b) If two lines are perpendicular, the product of their gradients must be .

In this case, . This condition can be applied to your answer in a).

If a quantity is independent of a variable it means that the value of the variable (whatever it may be) has no influence on what the quantity is.

For example, if then is independent of .

But, if then is NOT independent of .

 

[HeroWise]

 

[Danneo]

Thx for your working out , tho i lost track of whats going on in part ii) can you help me understand?

 

[fan96]

and, similarly, .



The intercept of can be found by setting in the equation of . This gives:



Which is independent of either parameter.