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Help with this C1 Maths Question Please.

The point P on the curve y = kÏx has x-coordinate 4. The normal to the curve at P is parallel to
the line 2x + 3y = 0.
(i) Find the value of k. [6]
(ii) This normal meets the x-axis at the point Q. Calculate the area of the triangle OPQ, where O is the point (0, 0).
I found out k which is 6, on part (ii) I have no idea how to get the point Q, I saw it on the markscheme however I just dont get how they got it.
Please Helppp!

btw that is k root x
(edited 9 years ago)
Reply 1
Original post by underestimate
The point P on the curve y = kÏx has x-coordinate 4. The normal to the curve at P is parallel to
the line 2x + 3y = 0.
(i) Find the value of k. [6]
(ii) This normal meets the x-axis at the point Q. Calculate the area of the triangle OPQ, where O is the point (0, 0).
I found out k which is 6, on part (ii) I have no idea how to get the point Q, I saw it on the markscheme however I just dont get how they got it.
Please Helppp!

btw that is k root x


I am trying to make sence of the question and I cannot see what Q is until the very end when the triangle OPQ appears?

why don't you send a photo of the question and some of your workings?


EDIT: I just saw the edit!
(edited 9 years ago)
Reply 2
find the equation of the normal at P
(you already have the gradient and you can find y coord)

then surely you can find where it crosses the x axis ... (set something to zero)
Original post by TeeEm
find the equation of the normal at P
(you already have the gradient and you can find y coord)

then surely you can find where it crosses the x axis ... (set something to zero)


Thanks I will try that :smile:.:smile:
Okay so the equation of the normal is y= -2/3x
When this line crosses the x axis, y = 0. However if I set y to 0, I would get x at 0. But the mark scheme says x is 22 and the co-ordinates of (22,0). How do I do this? I am so confused.
Original post by underestimate
Okay so the equation of the normal is y= -2/3x
When this line crosses the x axis, y = 0. However if I set y to 0, I would get x at 0. But the mark scheme says x is 22 and the co-ordinates of (22,0). How do I do this? I am so confused.

Note that the question says that the normal to the tangent at P is PARALLEL to the line with equation 2x+3y=0. You seem to be assuming that the normal has that equation too, when it will only have the same gradient as that line.
Knowing that the x-coordinate of P is 4, could you find the y-coordinate and use this to find the equation of the normal?
(edited 9 years ago)
Oh okay thanks, that makes sense! Cheers.

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