Core 4 Cartesian Equation Q

Please can someone help with part a of this question! Not really done these too much in class, trying to make T the subject of one equation but struggling. Thanks!

You don't always need to make $t$ the subject, sometimes there are less obvious but quicker and neater approaches.

For example, note that if you take the left equation and say $\dfrac{x}{t} = \dfrac{t^2}{t^2+1}$ then get that $\dfrac{x}{t} = y$

which we can square and rearrange to get $x^2 = t^2 y^2$

Also note that you can obtain $t^2$ entirely in terms of $y$ by rearranging for it in $y=\dfrac{t^2}{t^2+1}$

Okay thank you, I understand what you've said but still unsure of how to get the equation in the form they want? Where does the y^3 come from?

And also regarding your last point for rearranging the equation for t^2, how do you go about doing this?

If you work through it then it will become apparent where it comes from.

To rearrange for $t^2$, just start by getting rid off the denominator so that $y(t^2+1)=t^2$ hence $yt^2+y = t^2$ then factor out $t^2$ in the next step or so before getting it on its own.

Got it, thanks! On the first step you did, , by dividing both sides by T would you always divide the numerator by the T? I didn't think of this to do, never really done it before.

And one more thing (sorry for a million questions), I'm doing a question on implicit differentiation- and set dy/dx=0 and ended up with x + y - 1 = 0, all I have is the original equation of the curve, and no point- how can I go about solving this for the stationary points?

Thanks again