The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricit

₹0.0

Question: The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricity of the ellipse?

Options:

Correct Answer: 0.6

Solution:

Rewriting gives x^2/9 + y^2/4 = 1. Here, a^2 = 9, b^2 = 4, c = √(a^2 - b^2) = √(9 - 4) = √5. Eccentricity e = c/a = √5/3 ≈ 0.6.

The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricity of the ellipse?

The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricity of the ellipse?

Step 1: Start with the given equation of the ellipse: 4x^2 + 9y^2 = 36.
Step 2: Divide the entire equation by 36 to simplify it: (4x^2)/36 + (9y^2)/36 = 1.
Step 3: This simplifies to x^2/9 + y^2/4 = 1.
Step 4: Identify a^2 and b^2 from the equation: a^2 = 9 and b^2 = 4.
Step 5: Calculate c using the formula c = √(a^2 - b^2): c = √(9 - 4) = √5.
Step 6: Find the eccentricity e using the formula e = c/a: e = √5/3.
Step 7: Approximate the value of e: e ≈ 0.6.

Ellipse Properties – Understanding the standard form of an ellipse and how to derive its eccentricity from the semi-major and semi-minor axes.
Eccentricity Calculation – Calculating eccentricity using the formula e = c/a, where c is the distance from the center to a focus, and a is the semi-major axis.