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    Hi everyone, could someone explain the best way to go about this question to me please? I'm sure I'm missing something obvious but I just can't work it out

    parametric equations:
     x = 2cos(t)
     y = 3sin(t)

    i) Find the points of intersection with the axis (I can do this part)
    ii) Find the coordinates of the points for which the tangent to the curve cuts the x-axis at (4, 0).

    How would I do part ii?

    Thanks in advance
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    (Original post by kingkong95)
    Hi everyone, could someone explain the best way to go about this question to me please? I'm sure I'm missing something obvious but I just can't work it out

    parametric equations:
     x = 2cos(t)
     y = 3sin(t)

    i) Find the points of intersection with the axis (I can do this part)
    ii) Find the coordinates of the points for which the tangent to the curve cuts the x-axis at (4, 0).

    How would I do part ii?

    Thanks in advance
    I haven't tried it, but I think the first step would be to find a general equation for the tangent to the curve at a point described by parameter t.
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    (Original post by kingkong95)
    Hi everyone, could someone explain the best way to go about this question to me please? I'm sure I'm missing something obvious but I just can't work it out

    parametric equations:
     x = 2cos(t)
     y = 3sin(t)

    i) Find the points of intersection with the axis (I can do this part)
    ii) Find the coordinates of the points for which the tangent to the curve cuts the x-axis at (4, 0).

    How would I do part ii?

    Thanks in advance
    From the parametric equations
    \frac{x^2}{4}+\frac{y^2}{9}=1
    The equation of tangent line is
    y=m(x-4)
    Solve these equations simultaneously substituting the 2nd into the first one
    You vill get a quadratic equation for x with parameter of m.
    Consider that for x you can get only one solution because the line has
    one common point with the curve (ellipse).
    So in the formula for the quadratic equation the discriminant D=0
    From this equation you will get the value of m
    then finish the solution or find the point where the derivative is m
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    (Original post by davros)
    I haven't tried it, but I think the first step would be to find a general equation for the tangent to the curve at a point described by parameter t.
    (Original post by ztibor)
    From the parametric equations
    \frac{x^2}{4}+\frac{y^2}{9}=1
    The equation of tangent line is
    y=m(x-4)
    Solve these equations simultaneously substituting the 2nd into the first one
    You vill get a quadratic equation for x with parameter of m.
    Consider that for x you can get only one solution because the line has
    one common point with the curve (ellipse).
    So in the formula for the quadratic equation the discriminant D=0
    From this equation you will get the value of m
    then finish the solution or find the point where the derivative is m
    Thanks for the help! I'll try it now
 
 
 
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