To find the area enclosed by the ellipse given by \(4x^2 + 9y^2 = 36\), we first rewrite it in standard form. Divide the entire equation by 36:

["# How to Find the Area Enclosed by the Ellipse (4x^2 + 9y^2 = 36)", "Understanding the area enclosed by an ellipse is a fundamental concept in geometry and calculus. The ellipse is a stretched or compressed circle, and its area can be easily calculated once it’s expressed in standard form. In this article, we’ll walk through how to rewrite the given equation (4x^2 + 9y^2 = 36) into standard form and then use it to compute the enclosed area.", "---", "## Step 1: Rewrite the Equation in Standard Form", "The standard form of an ellipse centered at the origin is:", "[\n\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\n]", "where (a) is the semi-major axis, (b) is the semi-minor axis, and the area is given by (A = \pi a b).", "We begin with the given equation:", "[\n4x^2 + 9y^2 = 36\n]", "To convert this into standard form, divide both sides of the equation by 36:", "[\n\frac{4x^2}{36} + \frac{9y^2}{36} = 1\n]", "Simplify each term:", "[\n\frac{x^2}{9} + \frac{y^2}{4} = 1\n]", "Now the equation is in standard form:", "[\n\frac{x^2}{3^2} + \frac{y^2}{2^2} = 1\n]", "Here, (a^2 = 9) so (a = 3), and (b^2 = 4) so (b = 2). Both axes are positive, confirming this is an ellipse with a horizontal major axis since (a > b).", "---", "## Step 2: Calculate the Enclosed Area", "Using the standard formula for the area of an ellipse:", "[\nA = \pi a b\n]", "Substitute (a = 3) and (b = 2):", "[\nA = \pi \ imes 3 \ imes 2 = 6\pi\n]", "---", "## Conclusion", "The area enclosed by the ellipse (4x^2 + 9y^2 = 36) is (6\pi) square units. Rewriting the equation into standard form was essential to identify (a) and (b), enabling a direct application of the area formula. This method works for any ellipse and highlights the importance of standardizing equations in geometric analysis.", "Whether you're solving geometry problems, studying calculus, or applying mathematical concepts in engineering, mastering the conversion of conic sections to standard form is key to unlocking their area and other properties efficiently.", "---", "Keywords: ellipse area, find area of ellipse, standard form ellipse, (4x^2 + 9y^2 = 36\ area, geometry formula, standardize ellipse equation, area of ellipse formula, conic sections, mathematical derivation", "---", "Meta Description: Learn how to find the area enclosed by the ellipse (4x^2 + 9y^2 = 36) by converting it to standard form and applying (A = \pi a b). Step-by-step guide with examples."]