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If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the
If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?
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Practice Questions
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Q1
If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?
3, 4
4, 3
6, 8
8, 6
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Rewriting the equation in standard form gives (x^2/16) + (y^2/9) = 1, so semi-major axis a = 4 and semi-minor axis b = 3.
Questions & Step-by-step Solutions
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Q
Q: If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?
Solution:
Rewriting the equation in standard form gives (x^2/16) + (y^2/9) = 1, so semi-major axis a = 4 and semi-minor axis b = 3.
Steps: 7
Show Steps
Step 1: Start with the given equation of the ellipse: 9x^2 + 16y^2 = 144.
Step 2: Divide every term in the equation by 144 to simplify it.
Step 3: This gives us (9x^2)/144 + (16y^2)/144 = 1.
Step 4: Simplify each term: (x^2/16) + (y^2/9) = 1.
Step 5: Identify the denominators: 16 and 9. These represent a^2 and b^2 respectively.
Step 6: Calculate the semi-major axis (a) by taking the square root of the larger denominator: a = sqrt(16) = 4.
Step 7: Calculate the semi-minor axis (b) by taking the square root of the smaller denominator: b = sqrt(9) = 3.
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