El segmento que une los puntos A( - c, 0) y B(c, 0) es la base de un triangulo?

Sea el vértice opuesto C = (x, y).

Hallemos cada lado

<img src="https://tex.z-dn.net/?f=L_1%3Dd%28A%2CC%29%3D%5Csqrt%7B%28-c-x%29%5E2%2B%280-y%29%5E2%7D%3D%5Csqrt%7B%28c%2Bx%29%5E2%2By%5E2%7D%5C%5C%20%5C%5C%0AL_2%3Dd%28B%2CC%29%3D%5Csqrt%7B%28c-x%29%5E2%2By%5E2%7D" />

Medida de la mitad de la base AB <img src="https://tex.z-dn.net/?f=m%3Dc" />

Por dato tenemos <img src="https://tex.z-dn.net/?f=%5Csqrt%7B%28c%2Bx%29%5E2%2By%5E2%7D%5Ccdot%20%5Csqrt%7B%28c-x%29%5E2%2By%5E2%7D%3Dc%5E2%5C%5C%20%5C%5C%0A%5Csqrt%7Bx%5E2%2By%5E2%2Bc%5E2%2B2xc%7D%5Ccdot%5Csqrt%7Bx%5E2%2By%5E2%2Bc%5E2-2xc%7D%3Dc%5E2%5C%5C%20%5C%5C%0A%5Csqrt%7B%28x%5E2%2By%5E2%2Bc%5E2%29%5E2-%282xc%29%5E2%7D%3Dc%5E2%5C%5C%20%5C%5C%0A%28x%5E2%2By%5E2%2Bc%5E2%29%5E2-%282xc%29%5E2%3Dc%5E4%5C%5C%20%5C%5C%0Ax%5E4%2By%5E4%2Bc%5E4%2B2x%5E2y%5E2-2x%5E2c%5E2%2B2y%5E2c%5E2%3Dc%5E4%5C%5C%20%5C%5C%0Ax%5E4%2By%5E4%2B2x%5E2y%5E2-2x%5E2c%5E2%2B2y%5E2c%5E2%3D0%5C%5C%20%5C%5C%0A%28x%5E2%2By%5E2%29%5E2-2c%5E2%28x%5E2-y%5E2%29%3D0%5C%5C%20%5C%5C%20%0A%28x%5E2%2By%5E2%29%5E2%3D2c%5E2%28x%5E2-y%5E2%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cboxed%7B%0A%5Cbegin%20%7Bcases%7D%0A%5Cdfrac%7B%28x%5E2%2By%5E2%29%5E2%7D%7Bx%5E2-y%5E2%7D%3D2c%5E2~%2C~%28x%2Cy%29%5Cneq%20%280%2C0%29%5C%5C%20%5C%5C%0A%280%2C0%29~%2C~%28x%2Cy%29%3D%280%2C0%29%0A%5Cend%7Bcases%7D%0A%7D%7D" />

Una Lemniscata.