Originally Posted by

**free_to_fly** I'd like some help with this rather difficult question:

The tangents at $\displaystyle \

P(ct_1 ,\frac{c}{{t_1 }})

\$ and $\displaystyle \

Q(ct_2 ,\frac{c}{{t_2 }})

\$ to the rectangular hyperbola with equation $\displaystyle \

xy = c^2

\$ meet on the rectangular hyperbola with equation $\displaystyle \

xy = \frac{{c^2 }}{4}

\$. Prove that PQ is tangent to the curve with equation $\displaystyle \

xy = 4c^2

\$

I'm not really sure what I need to do to prove this statement, and I can't seem to find the equation of PQ. Any help would be greatly appreciated.