Turn on thread page Beta
    • Thread Starter
    Offline

    10
    ReputationRep:
    The line with equation mx-y-2=0 touches the circle with equation x^2+6x+y^2-8y=4. Find 2 possible values of m, giving your answers in exact form.


    I worked it out but i can't find the mark scheme to this worksheet. Can someone please answer it and check with me?

    I got 9+2root29 over 10 AND 9 - 2root29 over 10
    Offline

    21
    ReputationRep:
    Try the app “Socratic” if you’re stuck with maths, I find it really helpful
    Posted on the TSR App. Download from Apple or Google Play
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Mark jam)
    The line with equation mx-y-2=0 touches the circle with equation x^2+6x+y^2-8y=4. Find 2 possible values of m, giving your answers in exact form.


    I worked it out but i can't find the mark scheme to this worksheet. Can someone please answer it and check with me?

    I got 9+2root29 over 10 AND 9 - 2root29 over 10
    This is correct. (though it should be 'OR' and not 'AND')
    Offline

    9
    ReputationRep:
    Solving the simultaneous eqns, (sub y=mx-2 into quadratic), you get

    x^2(1+m^2) + x(6-12m) + 16 = 0

    Now use property of discriminant for this eqn: since the straight line is a tangent for each value of m, there is only one solution to this quadratic, (some say repeated roots); hence the discriminant for this quadratic is equal to zero.

    This gives

    80m^2 - 144m - 28 = 0
    which doesn't factorise, so completing the square, (or using the formula) gives

    m= 9/10 +/- 2root(29)/10

    Never certain about whether this is m = .... AND m = .... or m=... OR m=...
    I usually write a comma in between the answers ....

    hth
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 10, 2018

1,162

students online now

800,000+

Exam discussions

Find your exam discussion here

Poll
Should universities take a stronger line on drugs?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

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.