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In geometry, the **director circle** of an ellipse or hyperbola (also called the **orthoptic circle** or **Fermat–Apollonius circle**) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross each other.

The director circle of an ellipse circumscribes the minimum bounding box of the ellipse. It has the same center as the ellipse, with radius , where and are the semi-major axis and semi-minor axis of the ellipse. Additionally, it has the property that, when viewed from any point on the circle, the ellipse spans a right angle.^{[1]}

The director circle of a hyperbola has radius , and so, may not exist in the Euclidean plane, but could be a circle with imaginary radius in the complex plane.

The director circle of a circle is a concentric circle having radius times the radius of the original circle.

More generally, for any collection of points P_{i}, weights w_{i}, and constant C, one can define a circle as the locus of points X such that

The director circle of an ellipse is a special case of this more general construction with two points *P*_{1} and *P*_{2} at the foci of the ellipse, weights *w*_{1} = *w*_{2} = 1, and C equal to the square of the major axis of the ellipse. The Apollonius circle, the locus of points X such that the ratio of distances of X to two foci *P*_{1} and *P*_{2} is a fixed constant r, is another special case, with *w*_{1} = 1, *w*_{2} = –*r*^{ 2}, and *C* = 0.

In the case of a parabola the director circle degenerates to a straight line, the directrix of the parabola.^{[2]}

**^**Akopyan & Zaslavsky 2007, pp. 12–13**^**Faulkner 1952, p. 83

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*Projective Geometry*, Edinburgh and London: Oliver and Boyd - Hawkesworth, Alan S. (1905), "Some new ratios of conic curves",
*The American Mathematical Monthly*,**12**(1): 1–8, doi:10.2307/2968867, JSTOR 2968867, MR 1516260 - Loney, Sidney Luxton (1897),
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