In Exercises 1-18, graph each ellipse and locate the foci. (x^2)/(49)+(y^2)/(36)=1

Name: Problem 6, Chapter 10: Algebra and Trigonometry
Uploaded: 2020-06-05T13:34:56-08:00
Duration: 1 min 32 s
Channel: Ankit Gupta
Description: In Exercises 1-18, graph each ellipse and locate the foci. (x^2)/(49)+(y^2)/(36)=1

step 1 We have given an equation of ellipse x squared divided by 49 plus y square divided by 36 is equa

In Exercises 1-18, graph each ellipse and locate the foci....

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Key Concepts

Ellipse

An ellipse is a type of conic section that represents the set of all points in a plane where the sum of the distances to two fixed points (the foci) is constant. This curve is symmetric about both its major and minor axes, making it a fundamental shape in analytic geometry.

Standard Form of an Ellipse

The standard equation of an ellipse is written as (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center of the ellipse, a represents the semi-major axis, and b represents the semi-minor axis. This form makes it easier to identify the key features and graph the ellipse.

Vertices and Axes

The vertices of an ellipse are the intersection points of the ellipse with its major axis, and they are located a units away from the center along that axis. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest, perpendicular to the major axis through the center.

Foci of an Ellipse

The foci of an ellipse are two fixed points located along the major axis, and they are found using the relationship c² = a² - b², where c is the distance from the center to each focus. Determining the foci is crucial for understanding the geometric properties and applications of the ellipse.

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