Recently Added Math Formulas

· Solving logarithmic functions using Logarithmic Identities
· Determine the foci and the equation of a hyperbola
· Determine the area of a cirlce based on its perimeter
· Right Triangle Calculations
· Solving Second Degree Polynomials 2

Additional Formulas

· Solving Second Degree Polynomials
· Solving Second Degree Polynomials 2
· Right Triangle Calculations
· Determine the area of a cirlce based on its perimeter
· Determine the foci and the equation of a hyperbola
· How to determine the focus and directrix for a parabola
· Solving logarithmic functions using Logarithmic Identities

Current Location > Math Formulas > Math Examples & Tutorials > Determine the foci and the equation of a hyperbola

Determine the foci and the equation of a hyperbola

Find the foci and the equation of the hyperbola with the vertices (0,±1) and asymptote y = 2x

NOTE:

i. The hyperbola has foci (±c, 0), where c2 = a2 + b2,vertices (±a, 0), and asymptotes .

ii. The hyperbola has foci (0, ±c), where c2 = a2 + b2,vertices (0, ±a), and asymptotes .

Solution: From Note (ii), and given information in the example, we can see that a=1 and a/b = 2. Thus b=a/2 = 1/2 and c2 = a2 + b2 = 5/4. Te foci are and the equation of the hyperbola is given by y2 - 4x2 = 1.