InterviewSolution
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InterviewSolution
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Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.`16 x^2+y^2=16` |
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Answer» Given equation is, `16x^2+y^2 = 16` We will convert this equation into standard form. `=>16/16x^2+1/16y^2 = 1` `=> x^2/1+y^2/16 =1 ` So, this is our standard equation of ellipse with, `a = 1, b = 4` `c = sqrt(b^2-a^2) = sqrt(16-1) = sqrt15` Here, as `b gt a`, major-axis will be `Y-`axis. Now, foci will be `(0,+-c) = (0,+-sqrt15).` Vertices will be `(0,+-b) = (0,+-4).` Length of major-axis ` = 2b = 8` Length of minor axis ` = 2a = 2` Eccentricity `= c/b = sqrt15/4.` Length of latus rectum ` = 2a^2/b = 2**1/4 = 1/2.` |
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