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# FP1 Rectangular Hyperbola Help Needed

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1. this is the question. I've looked at the mark scheme but it misses out steps so I don't quite understand it. Please help:

The rectangular hyperbola H has equation xy = c^2, where c is a positive constant. The point P (ct, c/t) ,t ≠ 0, is a general point on H.

An equation for the tangent to H at P is given by:
y = (-1/t^2)x + (2c/t)

￼￼￼The points A and B lie on H. The tangent to H at A and the tangent to H at B meet at the point ( (−6/7)c , (12/7)c ).
Find, in terms of c, the coordinates of A and the coordinates of B.
￼￼
2. (Original post by Alicia Powell)
this is the question. I've looked at the mark scheme but it misses out steps so I don't quite understand it. Please help:

The rectangular hyperbola H has equation xy = c^2, where c is a positive constant. The point P (ct, c/t) ,t ≠ 0, is a general point on H.

An equation for the tangent to H at P is given by:
y = (-1/t^2)x + (2c/t)

￼￼￼The points A and B lie on H. The tangent to H at A and the tangent to H at B meet at the point ( (−6/7)c , (12/7)c ).
Find, in terms of c, the coordinates of A and the coordinates of B.
￼￼
Since the tangents meet at the specified point, then the coordinates of that point must satisfy the equation of the tangent.

So, sub them into the equation of the tangent and solve for the parameter t.

You'll get two possible values corresponding to the two points, A and B.

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