What is the length of the major axis of the ellipse whose equation is 10 x^2+20 y^2=200 ? (A) 3.

step 1 is 4x square plus 25 y square equals to 100. We can write this expression as 4x square divided b

What is the length of the major axis of the ellipse whose...

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Key Concepts

Major Axis

The major axis of an ellipse is its longest diameter, running through the center and aligned with the greater of the two semi-axis lengths. Its total length is given by 2a if a represents the semi-major axis, making it a critical feature for understanding the extent of the ellipse.

Converting Equations to Standard Form

Many ellipse equations are initially presented in a general quadratic form. To analyze the ellipse's properties, including the lengths of its axes, it is necessary to convert the equation to the standard form by dividing through by the appropriate constant. This manipulation clarifies the values of a² and b², which are crucial for further calculations.

Ellipse Standard Form

An ellipse in standard form is expressed as (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center, and a and b are the lengths of the semi-major and semi-minor axes, respectively. This form allows easy identification of the ellipse's key geometric properties, including its orientation and dimensions.

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