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

Find the vertices, transverse and conjugate axes, eccentricity, co-ord

1.	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» 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)`.