H2 math question

Jia Xun SG

Hi folks,do help me with this A level question if possible.:)

j89/p1/Q 16b

The para. equations of a curve are x=at,y=at^2,where 'a' is a constant.

The points P:(ap,ap^2) and Q:(aq,aq^2) lie on the curve.Find and simplify an expression in terms of p and q,for the gradient of the chord PQ.Deduce from your expression that the graduent of the tangent to the curve at P is 2p.

Apparently I can do both parts of the question seperately which is useless.

I have problems trying to find a suitable expression that can be used relevantly throughout the question.I appreciate all relevant help given and thank you all whole-heartedly.:)

Xxjordenx SG

Find the gradient by using (y1-y2)/(x1-x2) of points P and Q.

You will get q+p.

To Deduce and express, it's simple,

Just write, as Q is moving towards the point P, the gradient of the chord PQ tends to the gradient of tangent. Thus q –> p. So LimM(pq) q–>p = p+p = 2p.

Drawing out a rough sketch of the chord and graph helps in expression too.

wee_ws SG

Hi Jia Xun,

To deduce means you need to connect both parts together.

The approach that Xxjordenx (thanks for replying) described is precisely how the tangent was defined historically and yes, drawing helps a lot in visualising what a chord looks like.

Thanks.

Cheers,
Wen Shih