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maths-urgently needed

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A line through through the point (3,0) meet the variable line y=tx at right angle at the point P.
Find in terms of t, the co-ordinates of P

  • maths-urgently needed -

    P has coordinates (x,tx)
    The line from (3,0) to P has slope -1/t

    now, drop an altitude from P to the x-axis.

    tx/(x-3) = -1/t
    x = 3/(1+t^2)

    P = (3/(1+t^2), 3t/(1+t^2))

  • maths-urgently needed -

    line 1: y=tx
    line 2: y=-x/t +b
    but you know point 3,0 is on line 2
    0=-3/t + b or b=3/t
    line2: y=-x/t +3/t
    line1 y=tx
    set them equal
    tx=-x/t+3/t solve for x
    then solve for y.

  • maths-urgently needed -

    Thank u so much @steve and @bobpursley

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