Definition Of Hyperbola

Hyperbola is a conic section in which difference of distances of all the points from two fixed points (called `foci`) is constant.

More About Hyperbola

The general equation for hyperbola is .
The eccentricity (e) of a hyperbola is always greater than 1, e > 1.
The slope of asymptotes for both horizontal and vertical hyperbola is .

 

The equation for the horizontal hyperbola is .

Video Examples: Hyperbola
 

The equation for the vertical hyperbola is .
The foci of the hyperbola are (± ; c, 0).

Example of Hyperbola

Solved Example on Hyperbola

Ques: Choose the standard form of the equation for the hyperbola shown.

Choices:

Correct Answer: D

Solution:

Step 1: In the graph, 2c = 6 and 2a = 4 or c = 3, a = 2.
Step 2: c² = a² + b² [Pythagorean relation.]
Step 3: 9 = 4 + b² [Substitute 3 for c, 2 for a.]
Step 4: b² = 5
Step 5: Since the transverse axis is horizontal, the standard form of the hyperbola is  or.

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