What is the eccentricity of a hyperbola defined by the equation x^2/a^2 - y^2/b^

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Question: What is the eccentricity of a hyperbola defined by the equation x^2/a^2 - y^2/b^2 = 1?

Options:

Correct Answer: √(1 + b^2/a^2)

Solution:

The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).

What is the eccentricity of a hyperbola defined by the equation x^2/a^2 - y^2/b^2 = 1?

What is the eccentricity of a hyperbola defined by the equation x^2/a^2 - y^2/b^2 = 1?

Step 1: Identify the standard form of the hyperbola equation, which is x^2/a^2 - y^2/b^2 = 1.
Step 2: Recognize that in this equation, 'a' and 'b' are constants that define the shape of the hyperbola.
Step 3: Understand that the eccentricity (e) of a hyperbola is a measure of how much it deviates from being circular.
Step 4: Use the formula for the eccentricity of a hyperbola, which is e = √(1 + b^2/a^2).
Step 5: Substitute the values of 'a' and 'b' from the hyperbola equation into the formula to calculate the eccentricity.

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