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O Does the origin lie inside or outside the ellipse with equation (x – 4) 2 + 4(y - 3) 2 = 4?

O Does the origin lie inside or outside the ellipse with equation (x – 4) 2 + 4(y - 3) 2 = 4?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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.
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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