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# FP1 question watch

1. The point P ( a*(t^2) , 2at ) lies on a parabola with equation y^2=4ax, where a is a positive constant.
The equation of a normal to the parabola at P is y+xt = 2at+ (a* (t^3))

The normal to the parabola at P meets the parabola again at Q

Find. in terms of t, the co-ordinates of Q.

can someone tell me what substitution has to be made to proceed with the problem and why we have to make the substitution?
2. your normal line at the point P is and this line meets the parabola at P and Q so both points lie on this line AND the parabola . Here I've used T to show this T is variable, and the t in the first equation is fixed once we've picked a point P. Hence .

So on the parabola and .

So make the substitutions in the equations above, into the first equation, giving (try it first, then look below:

Spoiler:
Show

and solve for T in terms of T. Then, substituting the result into the equation of the parabola will give Q.17

3. (Original post by foolsihboy)
your normal line at the point P is and this line meets the parabola at P and Q so both points lie on this line AND the parabola . Here I've used T to show this T is variable, and the t in the first equation is fixed once we've picked a point P. Hence .

So on the parabola and .

So make the substitutions in the equations above, into the first equation, giving (try it first, then look below:

Spoiler:
Show

and solve for T in terms of T. Then, substituting the result into the equation of the parabola will give Q.17

Im finding it a little difficult to understand why one t is variable and one is not in the same equation...

Isn't the equation for the normal to a parabola, y+xt = 2at+ at^3 , for all the co-ordinates of the normal where each of these co-ordinates are generated from a distinct t value?
thanks!
4. (Original post by confuzzled92)
Im finding it a little difficult to understand why one t is variable and one is not in the same equation...

Isn't the equation for the normal to a parabola, y+xt = 2at+ at^3 , for all the co-ordinates of the normal where each of these co-ordinates are generated from a distinct t value?
thanks!
Do You think that P lies on the parabola for all t?

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