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#### DrunkenOldFool

##### New member

- Feb 6, 2012

- 20

If $l$ and $m$ are variable real numbers such that $5l^2+6m^2-4lm+3l=0$, then a variable line $lx+my=1$ always touches a fixed parabola, whose axis is paralell to the x-axis.

(a) Find the vertex of the parabola.

(b) Find the focus of the parabola.