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Determine the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1
Determine the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1.
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Practice Questions
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Q1
Determine the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1.
Circles
Ellipses with varying axes
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Parabolas
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The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with varying semi-major and semi-minor axes.
Questions & Step-by-step Solutions
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Q
Q: Determine the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1.
Solution:
The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with varying semi-major and semi-minor axes.
Steps: 5
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Step 1: Identify the equation given, which is x^2/a^2 + y^2/b^2 = 1.
Step 2: Recognize that this equation is in the standard form of an ellipse.
Step 3: Note that 'a' represents the semi-major axis (horizontal stretch) and 'b' represents the semi-minor axis (vertical stretch).
Step 4: Understand that as 'a' and 'b' change, the size and shape of the ellipse will change, creating a family of ellipses.
Step 5: Conclude that the equation represents a family of ellipses with different sizes based on the values of 'a' and 'b'.
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