Problem

Find the standard form of the equation of the ellipse and give the location of its foci.

Answer

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Answer

The foci of the ellipse are located at the points (±c, 0), where c is the distance from the center of the ellipse to each focus. The value of c can be found using the relationship: \[\boxed{c = \sqrt{a^2 - b^2}}\]

Steps

Step 1 ：The standard form of the equation of an ellipse centered at the origin with semi-major axis a and semi-minor axis b is given by: \[\boxed{\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1}\]

Step 2 ：The foci of the ellipse are located at the points (±c, 0), where c is the distance from the center of the ellipse to each focus. The value of c can be found using the relationship: \[\boxed{c = \sqrt{a^2 - b^2}}\]

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