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

    0
    ReputationRep:
    Im having trouble with these two problems.....

    Prove that the circle (x+4)^2 + (y-5)^2 = 8^2 lies completely inside the
    circle x^2 +y^2 +8x - 10y = 59




    The circle C has equation

    x^2 +y^2 - 10x + 4y +20 = 0

    Find the length of the tangent to C from the point (-4,4)
    • Study Helper
    Offline

    13
    (Original post by chowderspin)
    Im having trouble with these two problems.....

    Prove that the circle (x+4)^2 + (y-5)^2 = 8^2 lies completely inside the
    circle x^2 +y^2 +8x - 10y = 59
    Complete the squares on the second equation to get it into the same form as the first and something should strike you.


    The circle C has equation

    x^2 +y^2 - 10x + 4y +20 = 0

    Find the length of the tangent to C from the point (-4,4)
    The line joining the point to the centre of the circle, and the tangent line, together with a radius forms a right angle triangle. So work out the length of the two others and use pythagoras.
    Offline

    0
    ReputationRep:
    I still couldn't get it...
    CA(tangent point) = 3 [ Because its the radius ]
    CP i have as root117 (3root13) [C(5,-2) and P(-4,4) ... x difference = 9, y difference = 6. therefore CP = root(9^2 + 6^2)]
    Then Finally for A(tangent point)to P : root(3^2 + 117) = 3root14 =root126=11.2 [NOT 6ROOT3 OR 10.4 WHICH THE BOOK READS.]
    Offline

    16
    ReputationRep:
    (Original post by IanBlue)
    I still couldn't get it...
    CA(tangent point) = 3 [ Because its the radius ]
    CP i have as root117 (3root13) [C(5,-2) and P(-4,4) ... x difference = 9, y difference = 6. therefore CP = root(9^2 + 6^2)]
    Then Finally for A(tangent point)to P : root(3^2 + 117) = 3root14 =root126=11.2 [NOT 6ROOT3 OR 10.4 WHICH THE BOOK READS.]
    \sqrt{117} is the hypotenuse!

    Did you draw a diagram?
    Offline

    0
    ReputationRep:
    (Original post by TenOfThem)
    \sqrt{117} is the hypotenuse!

    Did you draw a diagram?


    AHHH, i did. but it was a plotter triangle on a slant - thanks, i have the correct answer now
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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