Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Vertices Of An Ellipse
In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…
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**Question 40:** Does the origin lie inside or outside the ellipse with the equation \((x - 4)^2 + 4(y - 3)^2 = 4\)? **Explanation:** This is a mathematical problem that asks whether the point (0,0), known as the origin, falls within the boundaries of the ellipse defined by the given equation. To determine this, substitute \(x = 0\) and \(y = 0\) into the equation and evaluate: 1. Substitute values: \((0 - 4)^2 + 4(0 - 3)^2\) 2. Calculate each term: - \((0 - 4)^2 = 16\) - \(4(0 - 3)^2 = 4 \times 9 = 36\) 3. Combine the results: \[16 + 36 = 52\] Since 52 is greater than 4, the origin lies outside the ellipse.
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Transcribed Image Text:**Question 40:** Does the origin lie inside or outside the ellipse with the equation \((x - 4)^2 + 4(y - 3)^2 = 4\)? **Explanation:** This is a mathematical problem that asks whether the point (0,0), known as the origin, falls within the boundaries of the ellipse defined by the given equation. To determine this, substitute \(x = 0\) and \(y = 0\) into the equation and evaluate: 1. Substitute values: \((0 - 4)^2 + 4(0 - 3)^2\) 2. Calculate each term: - \((0 - 4)^2 = 16\) - \(4(0 - 3)^2 = 4 \times 9 = 36\) 3. Combine the results: \[16 + 36 = 52\] Since 52 is greater than 4, the origin lies outside the ellipse.
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