3U Locus Question (1 Viewer)

bell531 · Aug 19, 2009

The point (T, 1/T) lies on the hyperbola y=1/x. Show that 3xy=4 is the equation of the locus of the midpoint of the line joining (T, 1/T) and (3T, 1/3T) as T varies.

Help needed...I have no idea how to show it.

hermand · Aug 19, 2009

you should be studying for mx2, not 1!! that said, i'll check this out for you.

hermand · Aug 19, 2009

alright,
$M=\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )$
$\therefore M=\left ( \frac{{T}+3T}{2},\frac{\frac{1}{T}+\frac{1}{3T}}{2} \right )$
$\therefore M=\left ( 2T,\frac{2}{3T} \right )$
$when\; x=2T, y=\frac{2}{3T}$
$\therefore T=\frac{x}{2}$
$\therefore y=\frac{2}{3\frac{x}{2}}$
$\therefore y=\frac{4}{3x}$
$\therefore 3xy=4$

bell531 · Aug 19, 2009

Brilliant as ever dani, I had a feeling it went something like this. Thanks for that

braunstar13 · Aug 19, 2009

Dani did it better than you

3U Locus Question (1 Viewer)

bell531

Member's Member 2008

hermand

je t'aime.

hermand

je t'aime.

bell531

Member's Member 2008

braunstar13

New Member

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