Conic constant
In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by K = − e 2 , {\displaystyle K=-e^{2},} where e is the eccentricity of the conic section. The equation for a conic section with apex at the origin and tangent to the y axis is y 2 − 2 R x + ( K + 1 ) x 2 = 0 {\displaystyle y^{2}-2Rx+(K+1)x^{2}=0} or alternately x = y 2 R + R 2 − ( K + 1 ) y 2 {\displaystyle x={\dfrac {y^{2}}{R+{\sqrt {R^{2}-(K+1)y^{2}}}}}} where R is the radius of curvature at x = 0.