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Ex 11.4, 6 - 49y2 - 16x2 = 784 Find foci, latus rectum - Hyperbola

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  1. Chapter 11 Class 11 Conic Sections
  2. Serial order wise
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Ex 11.4, 6 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y2 – 16x2 = 784 49y2 – 16x2 = 784 Dividing whole equation by 784 ﷐49﷮784﷯y2 – ﷐16﷮784﷯x2 = ﷐784﷮784﷯ ﷐𝑦2﷮16﷯ – ﷐𝑥2﷮49﷯ = 1 ﷐𝑦2﷮42﷯ – ﷐𝑥2﷮72﷯ = 1 ‘ So our equation is of the form ﷐﷐𝑦﷮2﷯﷮﷐𝑎﷮2﷯﷯ − ﷐﷐𝑥﷮2﷯﷮﷐𝑏﷮2﷯﷯ = 1 ∴ Axis of hyperbola is y-axis Comparing (1) and (2) a2 = 42 a = 4 b2 = 72 b = 7 Also, c2 = a2 + b2 c2 = 72 + 42 c2 = 49 + 16 c2 = 65 c = ﷐﷮𝟔𝟓﷯ Coordinates of focus is (0, ±c) = (0, ±﷐﷮65﷯) So, foci are (0, ﷐﷮65﷯) & (0, −﷐﷮65﷯) Coordinates of vertices = (0, ±a) = (0, ±4) So, co-ordinates of vertices are (0, 4) & (0, –4) Eccentricity is e = ﷐𝑐﷮𝑎﷯ = ﷐﷐﷮65﷯﷮4﷯ Latus rectum = ﷐2﷐𝑏﷮2﷯﷮𝑎﷯ = ﷐2 × ﷐7﷮2﷯﷮4﷯ = ﷐2 × 49﷮4﷯ = ﷐49﷮2﷯

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