Find the co-ordinates of vertices, length of major and minor axis, eccentricity, co-ordinates of foci, length of latus rectum, co-ordinates of the ends of latus rectum and equation of directrices of each of following ellipse. (i) (x^(2))/(16)+(y^(2))/(9)=1 , (ii) (x^(2))/(9)+(y^(2))/(16)=1 (iii) 16x^(2)+y^(2)=16 , (iv) x^(2)+4y^(2)=4

Find the co-ordinates of vertices, length of major and minor axis, ecc

1.	Find the co-ordinates of vertices, length of major and minor axis, eccentricity, co-ordinates of foci, length of latus rectum, co-ordinates of the ends of latus rectum and equation of directrices of each of following ellipse. (i) (x^(2))/(16)+(y^(2))/(9)=1 , (ii) (x^(2))/(9)+(y^(2))/(16)=1 (iii) 16x^(2)+y^(2)=16 , (iv) x^(2)+4y^(2)=4
Answer» Answer :(i) Vertices `=(pm4,0), major axis = 8, minor axis `=6,e=(sqrt(7))/(4)`, co-ordinates of foci `=(pmsqrt(7),0)`, length of latus rectum = `(9)/(2)`, co-ordinates of the end point of latus rectum `=(pmsqrt(7),pm(9)/(4))`,equation of directrices `x=pm(16)/(sqrt(7))` Vertices `=(0,pm4)`, major axis = 8, minor axis = 6, `e=(sqrt(7))/(4)`, co-ordinates of foci `=(0,pmsqrt(7))`, length of latus rectum `=(9)/(2)`, co-ordinates of the ends of latus `=(=m(9)/(4),pmsqrt(7))`, equation of directrices `y=pm(16)/(sqrt(7))` (iii) Vertex `(0,pm4)`, major axis =8 minor axis = 2, `e=(sqrt(15))/(4)`, co-ordinates of foci `=(0,pmsqrt(15))`, length of latus rectum `=(1)/(2)`, co-ordinates of the ends of latus rectum `=(pm(1)/(4),pmsqrt(15))`, equation of directrices `y=pm(16)/(sqrt(15))` (IV) Vertices `=(pm2,0)`, major axis =4 , minor axis = 2, e=(sqrt(3))/(2)`, co-ordinates of foci `=(pmsqrt(3),0)`, equation of directrices `x=pm(4)/(sqrt(3))`