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Math Help - im confused

  1. #1
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    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.
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  2. #2
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    Show that the line y = mx + c touches the circle x^2 + y^2 = a^2 if c^2 = a^2(1+m^2)
     x^2 + y^2 = a^2
     x^2 + (mx + c)^2 = a^2
     x^2 + m^2 x^2 + c^2+2mcx = a^2
     (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
     discriminant = 0
     d= (2mc)^2 -4(1 + m^2)(c^2- a^2)=0
    4a^2-4c^2+4m^2a^2=0
    c^2 = a^2+a^2m^2
    c^2 = a^2(1+m^2)
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  3. #3
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    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
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  4. #4
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    the equation of the tangent to the circle having centre at origin is given by
     x_{0}x+y_{0}y=r^2
     where (x_{0},y_{0}) are\ point\ of\ intersection
     since\ (p,q)\ lies\ on\ the\ circle\ x^2 + y^2 = a^2.
     therefore\ p^2 + q^2 = a^2 =(radius)^2
    therefore equation of the tangent
     px+qy= p^2 + q^2
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