# Hearth (mathematics)

One generally indicates by hearth one or more points characteristic associated with a remarkable figure of Géométrie.

### Case of the conical ones

The definition monofocale of a Conique jointly uses a hearth F and a line D called associated director . The conical one seems whole of the points M of the plan such as $\ \left\{D \left(M, F\right)\right\} = E \ \left\{D \left(M, D\right)\right\}$. According to the value of strictly positive reality E which one names eccentricity, the unit will be a ellipse, a Parabole or a hyperbole.
• the points of the parabola are thus characterized by property MF=MH on the diagram opposite, H indicating the projected orthogonal one of M on D.
• Plus the value E is close to 0, plus the conical one resembles a Cercle. Some estimate that the center of the circle is its hearth and that the director is rejected ad infinitum .

If the parabola has only one hearth, the ellipse and the hyperbole have each one of it two, allowing a bifocal definition of these curves. In the case of the ellipse, the sum of the distances from the points M to the two hearths is a constant; in the case of the hyperbole, it is the absolute value of the difference.

### Other plane curves

Others Courbe S plane are also seen allotting hearths , in particular if their points have properties related to the distances to these hearths. One can quote the case of the Lemniscate of Bernoulli, of the oval of Cassini, some Cubique S like the Strophoïde…

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