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# FP3 Ellipse and Hyperbola Q's help Watch

1. I have a 2 q's that i am struggling with, one on ellipse and one on a hyperbola. (struggle with latex plugin as well so here it goes without)

q1: The tangents to the ellipse x^2/a^2 + y^2/b^2 = 1 at the points P ( acos(theta), bsin(theta) ) and Q (-asin(theta), bcos(theta) ) intersect at the point R. As theta varies, show that R lies on the curve x^2/a^2 + y^2/b^2 = 2.

I have found the equations of the two tangents but i dont know where to go from there?

q2: A hyperbola x^2/(alpha)^2 - y^2/(beta)^2 = 1 has asymptotes with equation y^2=(mx)^2 and passes through the point (a,0). Find an equation in terms of x, y, a and m. (i have done this bit btw)
A point P on this hyperbola is equidistant from one of its asymptotes and the x axis. Prove that, for all values of m, P lies on the curve with equation (x^2-y^2)^2=4x^2(x^2-a^2)
Dont know where to start for this?
thanks for any help
2. (Original post by connoryoung)
I have found the equations of the two tangents but i dont know where to go from there?
Solve your simultaneous equations. You should get

x=a(cos(t)-sin(t))
y=b(cos(t)+sin(t))

From there it's easy to finish.

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