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Math Help - parametric dy/dx? can't factorise

  1. #1
    Member i_zz_y_ill's Avatar
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    parametric dy/dx? can't factorise

    curve eqn y^2+x^2=4

    (i) verify that x=t-t^-1 and y=t+t^-1 are paramtrics of that curve (DONE)

    (ii) show that dy/dx=((t-1)(t+1))/(t^2+1) in this form

    i did dy/dx=dy/dt x dt/dx
    = (1-t^-2)(1+t^2) i get stuck here getting into required form.

    or do 2ydy/dx + 2x = 0
    get: dy/dx = (t-t^-1)/(t+t^-1) stuck again

    im sure im just partially being stupid,, if n e one can spot how to factorise for me that'd be gr8 cheers
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  2. #2
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    y^2  + x^2  = 4 \Rightarrow \quad 2yy' + 2x = 0 \Rightarrow \quad \frac{{dy}}{{dx}} =  - \frac{x}{y}

    \frac{{dx}}{{dt}} = 1 + t^{ - 2} \,\& \,\frac{{dy}}{{dt}} = 1 - t^{ - 2}

    \frac{{dy}}<br />
{{dx}} = \frac{{1 - t^{ - 2} \,}}<br />
{{1 + t^{ - 2} }}\left( {\frac{{t^2 }}<br />
{{t^2 }}} \right) = \frac{{t^2  - 1}}<br />
{{t^2  + 1}}
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