Find your Math Personality!
Find your Math Personality!
Find an equation in standard form for the hyperbola with vertices at (0, ± 2) and foci at (0, ± 11).
Solution:
A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone.
The centre bisects the line joining the vertices (0, -2) and (0, 2)
C is the origin
Distance between the vertices is the transverse axis 2a = 4
⇒ a = 2
Distance between foci = 2a × eccentricity
So,
4e = 18
⇒ e = 9/2
Semi transverse axis b = a√(e2 - 1)
Substituting the values
b = 2√(81/4 - 1)
b = √77
a2 = 4 and b2 = 77
So the equation of the hyperbola is x2/4 - y2/77 = 1
Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11).
Summary:
An equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11) is x2/4 - y2/77 = 1.
Math worksheets and
visual curriculum
visual curriculum