# Parametrics question (1 Viewer)

#### TeheeCat

##### Active Member
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

##### 617 pages
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 .

• BLIT2014 and TeheeCat

#### HeroWise

##### Active Member  • BLIT2014 and TeheeCat

#### Danneo

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

#### fan96

##### 617 pages
and, similarly, .

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

Which is independent of either parameter.

• Danneo