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Determine the foci coordinates, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse (x 2 /49) + (y 2 /36) = 1

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2 months ago Anand Kumar Pandey
1677 Points
```							Welcome to AskIITiansThe given equation is (x^2/49) + (y^2/36) = 1It can be written as (x^2/7^2) + (y^2/6^2) = 1It is noticed that the denominator of x^2/49 is greater than the denominator of the y^2/36On comparing the equation with (x^2/a^2) + (y^2/b^2) = 1, we will geta= 7 and b = 6Therefore, c = √(a^2– b^2)Now, substitute the value of a and b⇒ √(a^2– b^2) = √(72– 62) = √(49-36)⇒ √13Hence, the foci coordinates are ( ± √13, 0)Eccentricity, e = c/a = √13/ 7Length of the major axis = 2a = 2(7) = 14Length of the minor axis = 2b = 2(6) =12The coordinates of the vertices are ( ± 7, 0)Latus rectum Length= 2b^2/a = 2(6)^2/7 = 2(36)/7 = 72/7Thanks
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2 months ago
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