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# Conics watch

1. The equation of the tangent to the rectangular hyperbola xy=(c^2) is at the point P(cp, (c/p)) is

x+yp²=2cp

The tangent to C at P meets the x-axis at the point X.

The point Q on C has coodinates (cq, (c/q)), q=/=p such that QX is parallel to the y-axis.

Show that q=2p.

Newton.
2. ok
for where P meets X
y = 0
x = 2cp
p = x/2c ------ 1

for Q
has same X when y = 0
so using eqn 1
p = cq/2c
2p = q

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