Determine if 252? + 16y² = 1 is an ellipse. O Not an Ellipse Ellipse, we can write the equation of the ellipse in standard form (x – h), (y – k)² - 1. Where: a? h = k = a = b =
Determine if 252? + 16y² = 1 is an ellipse. O Not an Ellipse Ellipse, we can write the equation of the ellipse in standard form (x – h), (y – k)² - 1. Where: a? h = k = a = b =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Example: Determining if an Equation Represents an Ellipse**
**Problem Statement:**
Determine if \( 25x^2 + 16y^2 = 1 \) is an ellipse.
**Solution:**
Select one of the following options:
- \( \bigcirc \) Not an Ellipse
- \( \bigcirc \) Ellipse, we can write the equation of the ellipse in standard form \(\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1 \). Where:
- \( h = \) [Text Box]
- \( k = \) [Text Box]
- \( a = \) [Text Box]
- \( b = \) [Text Box]
Checkmark icon indicates the correct answer for selecting the ellipse option.
For the given equation \( 25x^2 + 16y^2 = 1 \):
1. Identify the coefficients: \( A = 25 \), \( B = 16 \).
2. Compare with the standard form:
- The given equation divides by 1 (which is already in the given form of \( \frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} \)).
- This means \( a^2 = \frac{1}{25} \) and \( b^2 = \frac{1}{16} \).
3. Solving for \( a \) and \( b \):
- \( a = \frac{1}{5} \)
- \( b = \frac{1}{4} \)
4. The center (h, k) for this ellipse is (0, 0).
Therefore, the entry should be:
- \( h = 0 \)
- \( k = 0 \)
- \( a = \frac{1}{5} \)
- \( b = \frac{1}{4} \)
This confirms that \( 25x^2 + 16y^2 = 1 \) is indeed an ellipse in standard form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a7c8b7c-6421-40e7-b33a-5c89a0da3579%2F528974d1-bb90-47a6-8636-f427cfbd11ac%2Fi5hlvnv.png&w=3840&q=75)
Transcribed Image Text:**Example: Determining if an Equation Represents an Ellipse**
**Problem Statement:**
Determine if \( 25x^2 + 16y^2 = 1 \) is an ellipse.
**Solution:**
Select one of the following options:
- \( \bigcirc \) Not an Ellipse
- \( \bigcirc \) Ellipse, we can write the equation of the ellipse in standard form \(\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1 \). Where:
- \( h = \) [Text Box]
- \( k = \) [Text Box]
- \( a = \) [Text Box]
- \( b = \) [Text Box]
Checkmark icon indicates the correct answer for selecting the ellipse option.
For the given equation \( 25x^2 + 16y^2 = 1 \):
1. Identify the coefficients: \( A = 25 \), \( B = 16 \).
2. Compare with the standard form:
- The given equation divides by 1 (which is already in the given form of \( \frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} \)).
- This means \( a^2 = \frac{1}{25} \) and \( b^2 = \frac{1}{16} \).
3. Solving for \( a \) and \( b \):
- \( a = \frac{1}{5} \)
- \( b = \frac{1}{4} \)
4. The center (h, k) for this ellipse is (0, 0).
Therefore, the entry should be:
- \( h = 0 \)
- \( k = 0 \)
- \( a = \frac{1}{5} \)
- \( b = \frac{1}{4} \)
This confirms that \( 25x^2 + 16y^2 = 1 \) is indeed an ellipse in standard form.
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