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# Co-ordinate Geometry Help. :) C4 watch

1. Hi,

The parametric equations of the curve C are

x = 2t + 1, y = t^2 + 3.

- Show that the tangent to C at the point P with parameter p has equation

px - y = p^2 + p - 3. Ok, I've done this one. :P

- The tangent to C at the point P passes through the point (2, -3). Given that the point P is in the second quadrant, find the equation of the tangent.

I am really confused here. Ummm.. What is the second quadrant firstly? Also dont I already have the equation of the tangent in part a therefore would I just plug in the numbers?

Any help would be appreciated, thank you.
2. (Original post by Matthew2010)
Hi,

The parametric equations of the curve C are

x = 2t + 1, y = t^2 + 3.

- Show that the tangent to C at the point P with parameter p has equation

px - y = p^2 + p - 3. Ok, I've done this one. :P

- The tangent to C at the point P passes through the point (2, -3). Given that the point P is in the second quadrant, find the equation of the tangent.

I am really confused here. Ummm.. What is the second quadrant firstly? Also dont I already have the equation of the tangent in part a therefore would I just plug in the numbers?

Any help would be appreciated, thank you.
You do indeed just bung the numbers into your previous expression. you should get a quadratic in p, which you presumably can solve to find two alternative values of p (i haven't done this yet, but it would seem the easiest way forward). You then use the fact that P is in the second quadrant. The four quadrants of a graph are the four separate areas the axes divide the x-y plane into. If you call the one in the top right Q1, and then label them by going around anti-clockwise, then you have a number for each quadrant. so q2 is the one where x is negative and y is positive. using this info, you should be able to work out which value of p is the one you want, and thus find your equation...
3. (Original post by Matthew2010)
Hi,

The parametric equations of the curve C are

x = 2t + 1, y = t^2 + 3.

- Show that the tangent to C at the point P with parameter p has equation

px - y = p^2 + p - 3. Ok, I've done this one. :P

- The tangent to C at the point P passes through the point (2, -3). Given that the point P is in the second quadrant, find the equation of the tangent.

I am really confused here. Ummm.. What is the second quadrant firstly? Also dont I already have the equation of the tangent in part a therefore would I just plug in the numbers?

Any help would be appreciated, thank you.
The x and y axis of coordinate system divide the plane to four
quadrant. For the points of the first quadrant the two coordinates are positive.
For the second the x cordinate of any point is negative and the y is positive.
Substitute the given coordinates into the equation of the tangent.
You get the values of parameter p for the point P.
Calculate the x and y coordinate of P, and check wether is in the 2nd quadrant.

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