# Example 10 - Chapter 11 Class 11 Conic Sections

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 10 Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x2 + 4y2 = 36. Given 9x2 + 4y2 = 36 Dividing whole equation by 36 9𝑥2 + 4𝑦236 = 3636 936x2 + 4𝑦236 = 1 𝑥24 + 𝑦29 = 1 Since 4 < 9 Hence the above equation is of the form 𝑥2𝑏2 + 𝑦2𝑎2 = 1 Comparing (1) & (2) We know that c = a2−b2 c = 9−4 c = 𝟓 Co-ordinate of foci = (0, ± c) = (0, ± 5) So co-ordinates of foci (0, 5), & (0, −5) Vertices = (0, ± a) = (0, ± 3) So vertices are (0, 3) & (0, −3) Length of major axis = 2a = 2 × 3 = 6 Length of minor axis = 2b = 2 × 2 = 4 Eccentricity e = ca = 53 Length of latus rectum = 2b2a = 2 × 43 = 83

Chapter 11 Class 11 Conic Sections

Serial order wise

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