hyperbola

The Hyperbola

Definition

Hyperbola can be defined as the locus of point that moves such that the difference of its distances from two fixed points called the foci is constant. The constant difference is the length of the transverse axis, 2a.
 

General Equation

From the general equation of any conic (A and C have opposite sign, and can be A > C, A = C, or A

$Ax^2 - Cy^2 + Dx + Ey + F = 0 \,$ or
 

$\, x^2 - Cy^2 + Dx + Ey + F = 0$

 

Conic Sections

Definition
Conic sections can be defined as the locus of point that moves so that the ratio of its distance from a fixed point called the focus to its distance from a fixed line called the directrix is constant. The constant ratio is called the eccentricity of the conic.
 

46 - 47 Solved Problems in Maxima and Minima

Problem 46
Given point on the conjugate axis of an equilateral hyperbola, find the shortest distance to the curve.

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