Question

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match the equations of ellipses to their equivalent equations in standard form.

Answer 1

The mathematics question involves converting the equations of ellipses into their standard forms by rearranging the terms, completing the square, and identifying the center and axis lengths of the ellipse.

Step-by-step explanation:

The subject of this question is mathematics, specifically focusing on equations of ellipses and converting them into standard form. When working with ellipses, the standard form of the equation is typically written as:

\(\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\)

Here, \(h\) and \(k\) represent the coordinates of the center of the ellipse, and \(a\) and \(b\) represent the lengths of the semi-major and semi-minor axes, respectively.

Step-by-step explanation:

1. Identify the given equation of the ellipse that needs to be converted to standard form.
2. Rearrange the terms to group x's and y's together, and move the constant to the other side of the equation.
3. Complete the square for both the x's and the y's.
4. Divide by the coefficient that makes the equation equal to 1, and identify the values for \(h\), \(k\), \(a\), and \(b\).

Following these steps will help convert an equation of an ellipse into its corresponding standard form.