Question

What is Director circle?

Answer

Director circle is that when a pair of tangents intersects to a central conic which are at right angles to each other. The equation of the director circle is
$\left(\mathrm{ab}–h^2\right)\left(x^2+y^2\right)–2\left(\mathrm{hj}–\mathrm{bg}\right)x–2\left(\mathrm{gh}–\mathrm{af}\right)y+c\left(a+b\right)–\left(f^2+g^2\right)=0$

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