hi again, i have re written my question in a better way, sorry for the confusion.


i have figured out how to do a simple parametric - cartesian equation in the form of x and y here is what i have already done.

x = 2 t - 2 -----------------(1)
y = 3 t - 2 -----------------(2)

multiply (1) by 3 and (2) by 2.

3x = 6 t - 6 -----------------(3)
2y = 6 t - 4 -----------------(4)

eliminate t from the two eqns by subtracting (4) from (3)

3x - 2y = -6 + 4
3x - 2y = -2


in my exam i am assured i will need to know harder ones like this, but i cannot figure out how to do these.

Express the parametric equations x = t + 1 and y = -3 t² + 3 t as a Cartesian equation in just x and y.

i also need to simpify this in the form y = a x² + b x + c.

Any help would be great.

kind regards lakitu

If x = t+1, then rearranging gives t = x-1

We can then substitute (x-1) for t in the equation y = -3t² + 3t so that:

y = -3(x-1)² + 3(x-1)

Multiply out to give:

y = -3(x²-2x+1) + 3x -3

and further to give:

y = -3x² +6x -3 + 3x -3 = -3x² + 9x - 6

Factorising -3x² + 9x - 6 gives:

y = (-3x + 3)(x-2) OR -3(x-1)(x-2)

Solving for y=0 gives x= 1 or 2

Hehe, don't worry, it happens to all of us. I was beaten by 3 seconds not too long ago.

But eventually, you're going to beat someone by a tiny amount as well, and the universe will be restored.

thank you to both of you ! big help i understand it all

regards

lakitu