Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Can anyone please help me answer this question?
    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
    Offline

    20
    ReputationRep:
    (Original post by emul004)
    Can anyone please help me answer this question?
    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
    Offline

    0
    ReputationRep:
    (Original post by emul004)
    Can anyone please help me answer this question?
    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.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Study tools

Rosette

Essay expert

Learn to write like a pro with our ultimate essay guide.

Thinking about uni already?

Thinking about uni already?

See where you can apply with our uni match tool

Student chat

Ask a question

Chat to other GCSE students and get your study questions answered.

Creating

Make study resources

Create all the resources you need to get the grades.

Planner

Create your own Study Plan

Organise all your homework and exams so you never miss another deadline.

Resources by subject

From flashcards to mind maps; there's everything you need for all of your GCSE subjects.

Papers

Find past papers

100s of GCSE past papers for all your subjects at your fingertips.

Help out other students

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.