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The point P(at^2,2at), lies on the parabola C with equation y^2 = 4ax, where a is a positive constant.

a)Show that an equation of the tangent to C at P is ty = x + at^2.

The tangent to C at the point A and tangent to C at the point B meet at the point with coordinates(-4a, 3a).

b) Find, in terms of a, the coordinates of A and the coordinates of B.

I got part a right, but i have no clue how to start part B, can anyone help me please?
Original post by alesha98
The point P(at^2,2at), lies on the parabola C with equation y^2 = 4ax, where a is a positive constant.

a)Show that an equation of the tangent to C at P is ty = x + at^2.

The tangent to C at the point A and tangent to C at the point B meet at the point with coordinates(-4a, 3a).

b) Find, in terms of a, the coordinates of A and the coordinates of B.

I got part a right, but i have no clue how to start part B, can anyone help me please?


The point (-4a, 3a) lies on the tangents, try plugging that into the equation for the tangent.
Reply 2
Avatar for TeeEm
TeeEm
19
Original post by EricPiphany
The point (-4a, 3a) lies on the tangents, try plugging that into the equation for the tangent.


I heard you were banned ...
Original post by TeeEm
I heard you were banned ...


was. ye...
Reply 4
Avatar for alesha98
alesha98
OP
4
Original post by EricPiphany
The point (-4a, 3a) lies on the tangents, try plugging that into the equation for the tangent.

Where does it tell you that the point(-4a,3a) lies on the tangents to C at P?
Original post by alesha98
Where does it tell you that the point(-4a,3a) lies on the tangents to C at P?


The point P is a general point, substituting different values of t gives you different points on the curve.
So the point A, for example, is in the form of P for a particular value of t, and the same for B.
The tangent at A is given by the general form of the tangent with the particular value of t associated with A substituted in.

In this case we don't know the coordinates of A and B, or their associated values of t, only that a given point lies on their tangents.
(edited 8 years ago)
Original post by TeeEm
I heard you were banned ...


Holy... Don't expect me to be around much longer, they're already biting my ass. I got called out for using text speech or something like that.
Reply 7
Avatar for TeeEm
TeeEm
19
Original post by EricPiphany
Holy... Don't expect me to be around much longer, they're already biting my ass. I got called out for using text speech or something like that.


I am sorry to hear that.

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