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Find the length of major axis minor axis length of latest rectum and eccentricity of following ellipse 9x^2 +4y^2=36 |
Answer» Solutions:-The GIVEN is the ellipse x²/36 + y²/16 = 1. Here, The denominator of x²/36 is greater than the denominator of y²/16 Therefore, the major axis is along the x - axis. the minor axis is along the y - axis. On comparing the given equation with x²/a² + y²/b² = 1 We obtain a = 6 and b = 4 => c = √a² - b² = √(6)² - (4)² = √36 - 16 = √20 = 2√5 Therefore, The coordinates of the fouc are (2√5, 0) and (-2√5, 0) The coordinates of the vertices are (6, 0) and (-6, 0). Length of majar axis => 2A = 2 × 6 = 12 Length of minor axis => 2B = 2 × 4 = 8 Eccentricity , e = c/a => 2√5/6 => √5/3 Length of Latus rectum => 2b²/a => 2 × 16/6 => 16/3 Hence, the coordinates of the fouc are (2√5, 0) and (-2√5, 0), The coordinates of the vertices are (6, 0) and (-6, 0). Length of majar axis = 12. Length of minor axis = 8, Eccentricity = √5/3, And Length of Latus rectum = 16/3. |
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