Question

Question 1 Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola x^2/16 - y^2/9 = 1

Class X1 - Maths -Conic Sections Page 262

Answer 1

x²/16 - y²/9 = 1
x²/4² - y²/3² = 1 --------(1)

concept : if equation of hyperbola is in the form of x²/a² - y²/b² = 1 --------------(2),then,
transverse axis is along X - axis due to coefficient of x² of hyperbolic equation is positive .
vertices ( ±a , 0)
Foci ( ±c, 0) where c = √{a² + b²}
eccentricity ( e ) = c/a
latusrectum = 2b²/a

now, compare the equations (1) and (2) ,
a = 4 and b = 3
then , c = √{a² + b²} = √{4² + 3²} = 5

hence, vertices ( ±a , 0) = ( ± 4, 0)
Foci ( ± c , 0) = ( ±5, 0)
eccentricity ( e ) = c/a = 5/4
Latusrectum = 2b²/a = 2 × 9/4 = 9/2