Equations of a parabola

Symmetry 50. Intercepts 50. Asymptotes 50. Equations of Slope 51. Tangents 51. Equations of a Straight Line 52. Equations of a Circle 53. Equations of a Parabola 53. Equations of an Ellipse of Eccentricity e 54. Equations of a Hyperbola 55. Equations of Three-Dimensional Coordinate Systems 56. Equations of a Plane 56. Equations of a Line 57. Equations of Angles 57. Equation of a Sphere 57. Equation of an Ellipsoid 57. Equations of Hyperboloids and Paraboloids 58. Equation of an Elliptic Cone 59. Equation of an Elliptic Cylinder 59. 

Marcus theory. Prove the point that A = 4AGJ by making use of the analytic expressions for the equation of a parabola. The two equations should be those that describe the curves on the left side of Fig. 10-11. 

For any constant pressure P, equation 2.78 is the equation of a parabola, and therefore all surfaces of constant pressure are paraboloids of revolution. The free surface of the liquid is everywhere at the pressure P0 of the surrounding atmosphere and therefore is itself a paraboloid of revolution. Putting P = Pa in equation 2.78 for the free surface... 

The equation of a parabola with its axis parallel to the y axis and vertex at h, k) is... 

This is the equation of a parabola with the concave side toward the surface tension axis it has a maximum value of occurring at... 

Note that this is the equation of a parabola the relation predicted in the phenomenological studies covered earlier. 

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