1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Circle and tangient question, AS core 2

  1. May 21, 2006 #1
    Doing a core 2 maths question, realised i cant remember how to find where a tangient and circle meet.

    The circle equation provided in question was x^2 + y^2 -10x + 9 = 0

    same as (x - 5)^2 + y^2 = 4^2

    Question was:

    "Given that line l with gradient 7/2 is a tangient to the circle, and that l touches circle at point T

    find an equation that passes through the centre of the circle and T"

    i tried to find out where line and circle met but wasnt able too. In mark scheme they had a very easy way to do it (m1m2=-1 so gradient is -2/7 and you know the co-ordinates of the centre of the circle, so you use y-y1 = m(x-x1) )

    So, anyway i tried to put line and circle together and realised i couldnt... this is what i did how do you do it?

    What i first was say that the forumula of the straight line is 7/2x + c = y where c is a constant

    i then substituted that in the circle forumula to get (x-5)^2 + (7/2x + c)^2 = 4^2

    multiplied out to get (53/4)x^2 + (7c - 10)x + 9 + c^2 = 0

    since there can only be one result, b^2 - 4ac = 0 so

    (7c -10)^2 - 4 * (53/4) * (9 + c^2) = 0

    which ends up with

    102c^2 -140c + 577 = 0

    which does not have a result... :confused:
  2. jcsd
  3. May 21, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    HINT: The radius of a circle is always perpendicular to the tangent. What can you say about the gradient two perpendicular lines?

  4. May 21, 2006 #3
    Thats the method they used in the mark scheme:

    so gradient is -2/7, midpoint of circle is 5,0 and you get y = -2/7(x-5)

    But i realised that i didnt know how to get the equation of the original line or where it meets the circle, so i thought i should ask about that here (i really shouldnt have confused it by keeping original question in my post)
    Last edited: May 21, 2006
  5. May 21, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sorry, a missunderstanding on my part. Okay, you now have the equation of the line by using, y - y1 = m(x - x1). Now, if a line and a curve intersect their x and y co-ordinates must be equal at that point. Can you go from here?

  6. May 21, 2006 #5
    ahhh i get it now you do the line going through the centre of the circle... wont bother posting calculation but:

    x = 5 +/- (784/53)^0.5

    thanks for the help!
    Last edited: May 21, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Circle and tangient question, AS core 2
  1. Circle question (Replies: 1)

  2. Question on circle (Replies: 10)

  3. 2 circles (Replies: 2)