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# Maths Help-Calculus watch

The point P(2,1) is on the curve y=x^2-x-1.
(i) Find the equation of the tangent at the point P(2,1)
The normal at a point Q on the curve is parallel to the tangent at P.
(ii) State the gradient of the tangent at Q.
(iii) Find the co-ordinates of the point Q.

I have got up to part (iii) and now I am just stuck. Can someone please help me!

ThankYouu
2. (Original post by emul004)
The point P(2,1) is on the curve y=x^2-x-1.
(i) Find the equation of the tangent at the point P(2,1)
The normal at a point Q on the curve is parallel to the tangent at P.
(ii) State the gradient of the tangent at Q.
(iii) Find the co-ordinates of the point Q.

I have got up to part (iii) and now I am just stuck. Can someone please help me!

ThankYouu
What do you know about the point Q?
- You know the gradient of the tangent at Q (which you worked out in part ii)
- Which means you also know the gradient of the curve y = x^2 - x - 1 at the point Q (because it's the same - tangents always have the same gradient as the curve at the point of contact, a principle you used in part i).

So all you need to do is find the point on the curve at which the gradient (dy/dx) is equal to your answer to part ii. Differentiate and equate
3. (Original post by emul004)
The point P(2,1) is on the curve y=x^2-x-1.
(i) Find the equation of the tangent at the point P(2,1)
The normal at a point Q on the curve is parallel to the tangent at P.
(ii) State the gradient of the tangent at Q.
(iii) Find the co-ordinates of the point Q.

I have got up to part (iii) and now I am just stuck. Can someone please help me!

ThankYouu
Think about what the answer to (ii) means, especially in relation to f'(x) - the gradient function.

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