Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi, Can anyone please help me through this GCSE Maths question stage by stage with the working out cos I really don't know how to do it!!!

    The straight line with the equation y=x+6 meets the circle with the equation x^2+y^2=50 at two points P and Q.

    By solving two simutaneous equations, find the coordinates of P and Q.

    (No graph paper provided btw)
    Offline

    1
    ReputationRep:
    (Original post by kieshaxxx)
    Hi, Can anyone please help me through this GCSE Maths question stage by stage with the working out cos I really don't know how to do it!!!

    The straight line with the equation y=x+6 meets the circle with the equation x^2+y^2=50 at two points P and Q.

    By solving two simutaneous equations, find the coordinates of P and Q.

    (No graph paper provided btw)
    Sub all instances of y with x+6 therefore:

    x^2+y^2=50 becomes x^2+(x+6)^2=50 expand and solve the quadratic.
    Offline

    2
    ReputationRep:
    When the line and the circle meet, they will have the same x and y co-ordinates so they are simultaneous equations. If you substitute the eqn of the line into the eqn of the circle, you get x^2 + (x+6)^2 = 50
    x^2 + x^2 + 12x + 36 = 50
    2x^2 + 12x - 14 = 0
    x^2 + 6x - 7 = 0
    (x+7)(x-1) = 0
    So either x = 1 or x = -7
    Substitute back into the equation of the line, at x = 1, y = 1+6=7, at x = -7, y = -7+6 = -1 so they meet at (1,7) and (-7,-1) You can check these points are right by making sure they lie on the circle (sub into left hand side, check the answer is 50)
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Bezza)
    x^2 + (x+6)^2 = 50
    x^2 + x^2 + 12x + 36 = 50
    2x^2 + 12x - 14 = 0
    x^2 + 6x - 7 = 0
    (x+7)(x-1) = 0
    So either x = 1 or x = -7
    Substitute back into the equation of the line, at x = 1, y = 1+6=7, at x = -7, y = -7+6 = -1 so they meet at (1,7) and (-7,-1) You can check these points are right by making sure they lie on the circle (sub into left hand side, check the answer is 50)

    I don't understand what you did after subbing the x+6 into the circle equation .... sorry I'm a bit slow when it comes to maths!
    Offline

    2
    ReputationRep:
    (Original post by kieshaxxx)
    I don't understand what you did after subbing the x+6 into the circle equation .... sorry I'm a bit slow when it comes to maths!
    Multiply out the brackets (x+6)^2 = (x+6)(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36, then I just added on the other x^2 and took 50 away from both sides. As all the numbers are even you can divide by 2, then factorise the quadratic equation.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Bezza)
    Multiply out the brackets (x+6)^2 = (x+6)(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36, then I just added on the other x^2 and took 50 away from both sides. As all the numbers are even you can divide by 2, then factorise the quadratic equation.
    Ahhhh .... thankyou soooo much!!! I get it now, and it's easy oH and worth 5 marks! I could always do with an extra 5 marks!
    Offline

    10
    ReputationRep:
    (Original post by kieshaxxx)
    Ahhhh .... thankyou soooo much!!! I get it now, and it's easy oH and worth 5 marks! I could always do with an extra 5 marks!
    If asked about the geometric significance of the equations:

    X² + Y² = 50 is a circle around the origin with radius √50.

    And Y = X + 6 is just a straight line gradient one and y intercept 6.
 
 
 
Turn on thread page Beta
Updated: June 5, 2004

University open days

  1. University of Cambridge
    Christ's College Undergraduate
    Wed, 26 Sep '18
  2. Norwich University of the Arts
    Undergraduate Open Days Undergraduate
    Fri, 28 Sep '18
  3. Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 29 Sep '18
Poll
Which accompaniment is best?
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.