Results 1 to 2 of 2

Math Help - Vector Calculus - please help!

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    11

    Vector Calculus - please help!

    Two circles have equations

    x^2 + y^2 + 2ax + 2by + c = 0

    and

    x^2 + y^2 + 2a'x + 2b'y + c' = 0

    Show that these circles are orthogonal if 2aa' + 2bb' = c + c'


    I'm assuming you have to grad both of these to get an expression for the vector normal to the tangent at any point on each circle. However I am unsure of how to finish - I thought of dot producting them and setting this to zero, but would this be correct, as this would mean the radii/tangents are perpendicular no matter which points they were taken?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by joker_900 View Post
    Two circles have equations

    x^2 + y^2 + 2ax + 2by + c = 0

    and

    x^2 + y^2 + 2a'x + 2b'y + c' = 0

    Show that these circles are orthogonal if 2aa' + 2bb' = c + c'

    ...
    Hello,

    1. The 2 circles must intersect therefore |\overrightarrow{M_1 M_2}|< r_1 + r_2..........That means you have to calculate first the radii and the distance between the 2 centers.

    2. The tangent of the first circle must pass through the center of the second circle and the tangent of the second circle must pass threough the center of the first circle to get perpendicular tangents. (see attachment)

    3. Thus (r_1)^2 + (r_2)^2 = (|\overrightarrow{M_1 M_2}|)^2 ......... After a few steps of transformation you should get the given result.

    4. Good luck!
    Attached Thumbnails Attached Thumbnails Vector Calculus - please help!-zweikrs_senkr_tang.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector Calculus (Position Vector)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 23rd 2011, 01:43 PM
  2. Vector Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 25th 2011, 09:09 AM
  3. Vector Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 30th 2010, 06:21 PM
  4. vector calculus - vector feilds
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 25th 2010, 01:17 AM
  5. Vector Calculus
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 27th 2008, 07:34 PM

Search Tags


/mathhelpforum @mathhelpforum