We appreciate your visit to Find the equation of the ellipse having the vertex at 13 0 the focus at 12 0 and the center at 0 0 A tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The equation of the ellipse is A) 25x² + 169y² = 4225.
Explanation:
To find the equation of an ellipse, we need to know the center, vertices, and one focus of the ellipse. Since the center is given as (0,0), we can use the distance formula to find the distance between the center and the vertex:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the values, we get:
d = √((0 - 13)² + (0 - 0)²) = √169 = 13
Therefore, the major axis of the ellipse is 2a = 26.
The equation of the ellipse with center (0,0) and major axis 26 is:
x²/a² + y²/b² = 1
Since the focus is (12,0), we know that a = 13, so we can substitute the values into the equation to get:
x²/13² + y²/b² = 1
Simplifying the equation, we get:
x²/169 + y²/b² = 1
Since the vertex is (13,0), we know that the distance from the center to the vertex is a, which is 13. The value of b can be found using the equation b² = a² - c², where c is the distance from the center to the focus:
b² = a² - c²
b² = 169 - 12²
b² = 169 - 144 = 25
So, the equation of the ellipse is:
25x² + 169y² = 4225
Learn more about Equation of an ellipse here:
https://brainly.com/question/35505037
#SPJ11
Thanks for taking the time to read Find the equation of the ellipse having the vertex at 13 0 the focus at 12 0 and the center at 0 0 A tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
