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26 January, 12:04

A circle has center at (7, 0). What is the equation of the line that is tangent to the circle at (2, 0) ?

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  1. 26 January, 14:59
    0
    First find equation

    center is (h, k) then

    (x-h) ^2 + (y-k) ^2=r^2

    given

    (7,0) is center

    (x-7) ^2+y^2=r^2

    also given (2,0)

    (2-7) ^2+0^2=r^2

    (-5) ^2=r^2

    25=r^2

    (x-7) ^2+y^2=25 is equation

    take derivitive of both sides, implicit differntiaton

    2 (x-7) + 2y dy/dx=0

    2 (x-7) = - 2y dy/dx

    (7-x) / y=dy/dx

    at (2,0)

    (7-2) / 0

    undefined

    that means the line is x=something

    (2,0)

    the equation is x=2
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