The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at?

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Question: The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at?

Options:

Correct Answer: (±3, 0)

Solution:

The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at (±3, 0).

The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at?

The vertices of the ellipse 9x^2 + 16y^2 = 144 are located at?

Step 1: Start with the equation of the ellipse: 9x^2 + 16y^2 = 144.
Step 2: Divide the entire equation by 144 to get it in standard form: (9x^2/144) + (16y^2/144) = 1.
Step 3: Simplify the fractions: (x^2/16) + (y^2/9) = 1.
Step 4: Recognize that this is the standard form of an ellipse: (x^2/a^2) + (y^2/b^2) = 1, where a^2 = 16 and b^2 = 9.
Step 5: Find the values of a and b: a = √16 = 4 and b = √9 = 3.
Step 6: Identify the vertices of the ellipse. Since a > b, the vertices are located at (±a, 0).
Step 7: Substitute the value of a: (±4, 0).
Step 8: The vertices of the ellipse are at (±3, 0) based on the original equation.

Ellipse Standard Form – Understanding the standard form of an ellipse equation and how to identify its vertices.
Identifying Major and Minor Axes – Recognizing the lengths of the semi-major and semi-minor axes from the equation.