Question

Find the vertices, transverse and conjugate axes, eccentricity, co-ordinates of foci, equation of directrices and length of latus rectum for each of the following hyperbola.
(i) `(x^(2))/(16)+(y^(2))/(9)=1`
(ii) `9x^(2)-4y^(2)=36`
(iii) `16y^(2)-9x^(2)=576`
(vi) `49x^(2)-16y^(2)=784`

Answer 1

Correct Answer - (i) Vertices `=(pm4,0), transverse axis = 8, conjugate axis = 6, `e=(5)/(4)`, foci `=(pm5,0)`, equation of directrices `x=pm(16)/(5)`, latus rectum `=(9)/(2)`
(ii) Vertices `=(pm2,0)`, transverse axis = 12, conjugate axis = 16 , `(sqrt(13))/(2)`, foci `=(pmsqrt(13),0)`, equation of directrices `x=pm(4)/(sqrt(13))`, latus rectum =9
(iii) Vertices `=(0,pm6)`, transverse axis = 12 conjugate axis =16, `e=(5)/(3)`, foci = `(0,pm10)`, equation of directrices `y=pm(18)/(5)`, latus rectum `=(64)/(3)`
(iv) Vertices `=(pm4,0)`, transverse axis = 8, conjugate axis = 14, `e=(sqrt(65))/(4),foci `=(pmsqrt(65),0)`, equation of directrices `x=pm(16)/(sqrt(65))`, latus rectum `=(49)/(2)`.