


Hyperbola
Last updated at Dec. 16, 2024 by Teachoo
Transcript
Example 14 Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas: (i) x2/9 â y2/16 = 1, The given equation is đĽ2/9 â đŚ2/16 = 1 The above equation is of the form đĽ2/đ2 â đŚ2/đ2 = 1 Comparing (1) & (2) a2 = 9 a = 3 & b2 = 16 b = 4 Also, c2 = a2 + b2 c2 = 9 + 16 c2 = 25 c = 5 So, Co-ordinate of foci = (Âąc, 0) = (Âą5, 0) Thus, Co-ordinate of foci are (5, 0) & (â5, 0) Vertices = (Âąa, 0) = (Âą3, 0) Thus, Vertices are (3, 0) & (â3, 0) Eccentricity e = đ/đ = đ/đ Latus rectum = 2đ2/đ = (2 Ă 16)/3 = đđ/đ