1.
Working With Hyperbolas
(you have to know where to look)
urban geometry hyperbolas by ﬂickr user johncarney
2.
The Standard Form for the Equation of a Hyperbola
Horizontal Orientation Vertical Orientation
Differences
Similarities
• numerators have different
• have the same terms orientation
• both equal 1 • numerators have
• both are differences opposite signs
• both have same denominators
• both have square binomials
• (h, k) indicates center
3.
The Anatomy of The Hyperbola P
B1
b c F
F2 a 1
A 1 O c A2
B2
O is the centre, it has coordinates (h, k).
A1A2 is the length of the B1 B2 is the length of the
transverse axis. It's length is 2a. conjugate axis. It's length is 2b.
PF1 & PF 2 are the focal F 1 & F 2 are called the foci. They
radii of the hyperbola. are c units from the centre.
OA1 = OA2 is the length of the A1 & A 2 are called the
semitransverse axis with length a. vertices of the hyperbola.
OB1 = OB2 is the length of the B 1 & B 2 are called the endpoints
semiconjugate axis with length b. of the conjugate axis.
4.
Horizontal Hyperbola Vertical Hyperbola
a b a
O
O b
5.
The Pythagorean Property
B1
b a c
F1
F2 A2 O c A 1
B2
2 2 2
c = a +b
Horizontal Hyperbola Vertical Hyperbola
7.
For the hyperbola whose equation is given below.
(i) Write the equation in standard form
(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.
(iii) Sketch a graph of the hyperbola.
8.
For the hyperbola whose equation is given below.
(i) Write the equation in standard form
(ii) Determine the lengths of the transverse and conjugate axes, the
coordinates of the verticies and foci, and the equations of the asymptotes.
(iii) Sketch a graph of the hyperbola. SLOPE INTERCEPT FORM
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