If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the

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Question: If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?

Options:

Correct Answer: 3, 4

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.

If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?

If the equation of an ellipse is 9x^2 + 16y^2 = 144, what are the lengths of the semi-major and semi-minor axes?

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.

Ellipse Standard Form – Understanding how to convert the general equation of an ellipse into its standard form to identify the lengths of the semi-major and semi-minor axes.
Axes Lengths – Identifying the semi-major and semi-minor axes from the standard form of the ellipse equation.