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Standard Equations of Hyperbola

75586.png
75580.png
 
Transverse axis x-axis
Conjugate axis y-axis
Center (0, 0)
Length of transverse axis 2a
Length of conjugate axis 2b
Foci (± ae, 0)
Equation of directrices x = ± a/e
Relation in ab, and e b2 = a2(e2 – 1)
Length of latus rectum 75556.png
Parametric coordinates (a sec φb tan φ), 0 ≤ φ < 2π
Focal radii of any point P(x1y1) on the curve SP = ex1 – a and SP = ex1 + a
Difference of focal radii, SP – SP 2a

75574.png or 75568.png
 
75562.png 
 
Transverse axis y-axis
Conjugate axis x-axis
Center (0, 0)
Length of transverse axis 2b
Length of conjugate axis 2a
Foci (0, ± be)
Equation of directrices y = ± b/e
Relation in ab, and e a2 = b2(e2 – 1)
Length of latus rectum 75550.png
Parametric coordinates (b sec φa tan φ), 0 ≤ φ < 2π
Focal radii of any point P(x1y1) on the curve SP = ey1 – b and SP = ey1b
Difference of focal radii, SP – SP 2b





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