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For the ellipse defined by the equation 9x^2 + 16y^2 = 144, what are the lengths
For the ellipse defined by the equation 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
For the ellipse defined by the equation 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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The semi-major axis is 4 and the semi-minor axis is 3 after rewriting the equation in standard form.
Questions & Step-by-step Solutions
1 item
Q
Q: For the ellipse defined by the equation 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?
Solution:
The semi-major axis is 4 and the semi-minor axis is 3 after rewriting the equation in standard form.
Steps: 7
Show Steps
Step 1: Start with the given equation of the ellipse: 9x^2 + 16y^2 = 144.
Step 2: Rewrite the equation in standard form by dividing everything by 144.
Step 3: After dividing, the equation becomes (9x^2 / 144) + (16y^2 / 144) = 1.
Step 4: Simplify the fractions: (x^2 / 16) + (y^2 / 9) = 1.
Step 5: Identify the values from the standard form (x^2/a^2) + (y^2/b^2) = 1, where a^2 = 16 and b^2 = 9.
Step 6: Calculate a and b: a = sqrt(16) = 4 and b = sqrt(9) = 3.
Step 7: Determine which is the semi-major axis and which is the semi-minor axis: The semi-major axis is 4 and the semi-minor axis is 3.
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