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FP1 - parabola question

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

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

Find in terms of a, the coordinates of A and the coordinates of B anyone know where to start with this question?
Reply 1
Avatar for Scott3142
Scott3142
The first thing to do would be draw a diagram detailing what you know. You should then be able to work from the point of intersection to find your points A and B, as these are the only points of intersections of the tangent lines with C.
Reply 2
Avatar for ztibor
ztibor
10
doin' your mum
The point P(at^2 , 2at) lies on the parabola C with equation y^2 = 4ax, where a is a positive constant. The tangent to C at P is ty = x + at^2

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

Find in terms of a, the coordinates of A and the coordinates of B anyone know where to start with this question?


Create the equation of tangent line in form of
y=m(x+4a)+3a
where m is the gradient parameter
Solve this and the y^2=4ax equations simultaneously.
Take the discriminant of quadratic equation you got for x equal with zero because the line will tangent if there will be on solution for x, that is one common point with the parabola.
This give you 2 values for m. From these gradients and the derivative of
the parabola you can determine the coordiantes of A and B on the parabola.

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