Results 1 to 4 of 4

Thread: im confused

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    3

    im confused

    helloo i need to get an answer for this question

    Show that the line y = mx + c touches the circle x^2 + y^2 = a^2 if c^2 = a^2(1+m^2)

    it's very hard for me i need some help plz.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2009
    From
    New Delhi
    Posts
    153
    Show that the line y = mx + c touches the circle x^2 + y^2 = a^2 if c^2 = a^2(1+m^2)
    $\displaystyle x^2 + y^2 = a^2$
    $\displaystyle x^2 + (mx + c)^2 = a^2$
    $\displaystyle x^2 + m^2 x^2 + c^2+2mcx = a^2$
    $\displaystyle (1 + m^2) x^2 +2mcx + (c^2- a^2)=0$

    if the line y = mx + c touches the circle(or tangent to the circle) then
    $\displaystyle discriminant = 0 $
    $\displaystyle d= (2mc)^2 -4(1 + m^2)(c^2- a^2)=0$
    $\displaystyle 4a^2-4c^2+4m^2a^2=0$
    $\displaystyle c^2 = a^2+a^2m^2$
    $\displaystyle c^2 = a^2(1+m^2)$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    3
    Any help about this also?

    The point (p,q) lies on the circle x^2 + y^2 = a^2.
    Show that the equation of the tangent to the circle at (p,q) is px + qy = a^2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    May 2009
    From
    New Delhi
    Posts
    153
    the equation of the tangent to the circle having centre at origin is given by
    $\displaystyle x_{0}x+y_{0}y=r^2$
    $\displaystyle where (x_{0},y_{0}) are\ point\ of\ intersection$
    $\displaystyle since\ (p,q)\ lies\ on\ the\ circle\ x^2 + y^2 = a^2.$
    $\displaystyle therefore\ p^2 + q^2 = a^2 =(radius)^2$
    therefore equation of the tangent
    $\displaystyle px+qy= p^2 + q^2 $
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Jan 10th 2010, 08:45 AM
  2. confused.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Nov 14th 2009, 05:29 AM
  3. help!!!!!!!!!!!! so confused
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Jan 27th 2008, 01:54 PM
  4. confused :(
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Jan 23rd 2008, 06:25 PM
  5. Confused on what to do here..
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Jan 23rd 2008, 02:34 PM

Search tags for this page

Search Tags


/mathhelpforum @mathhelpforum