For the ellipse defined by the equation 9x^2 + 16y^2 = 144, what are the lengths

₹0.0

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

Options:

Correct Answer: 3, 4

Solution:

The semi-major axis is 4 and the semi-minor axis is 3 after rewriting the equation in standard form.

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

For the ellipse defined by the equation 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: 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.

Ellipse Standard Form – Understanding how to rewrite the equation of an ellipse in standard form to identify the lengths of the semi-major and semi-minor axes.
Identifying Axes – Recognizing which axis is the semi-major and which is the semi-minor based on the coefficients in the standard form.