DrunkenOldFool
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Find the equations of the sides of square inscribed in the circle $3(x^2+y^2)=4$, one of whose sides is parallel to the line $x-y=7$.
Opalg said:(click on the diagram to embiggen it).
It comes from The Simpsons. (f)Ackbach said:Great word!
Opalg said:With problems like this, it's always good to draw a diagram (click on the diagram to embiggen it).
[graph]psuayl2bwh[/graph]
The line $x-y=7$ has gradient 1, so the sides of the square will have gradient 1 and $-1.$ The circle is centred at the origin and has radius $2/\sqrt3$, so the vertices of the square will be at the points $(\pm2/\sqrt3,0)$ and $(0,\pm2/\sqrt3).$ You want the equations of the lines with gradient $\pm1$ going through those points, and with that information you can write down the answers.