`(x^(2))/(36)+(y^(2))/(16)=1`

Find the eccentricity of the ellipse (i) (x^(2))/(16)+(y^(2))/(9)=1 (ii) (x^(2))/(64)+(y^(2))/(36)=1

Find the eccentricity of the ellipse (i) (x^(2))/(16)+(y^(2))/(9)=1 (ii) (x^(2))/(64)+(y^(2))/(36)=1 (iii)25x^(2)+4y^(2)=100

Statement 1: Two ellipses (x^(2))/(16)+(y^(2))/(9)=1 and (x^(2))/(9)+(y^(2))/(16)=1 are congruent.Statement 2:(x^(2))/(16)+(y^(2))/(16)=1 and (x^(2))/(9)+(y^(2))/(16)=1 have same eccentricity

Find the co-ordinates of the vertices, the foci, the eccentricity and the length of latus-rectum of the hyperbolas : (a) (x^(2))/(9) -(y^(2))/(16) = 1 (b) (i) 16x^(2) - 9y^(2) = 576 (ii) y^(2) -16x^(2) = 1 (iii) 5y^(2) - 9x^(2) = 36 (iv) 49y^(2) - 16x^(2) = 784 .

The length of common tangent to the ellipses (x^(2))/(16)+(y^(2))/(9)=1 and (x^(2))/(9)+(y^(2))/(16)=1 is

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 and the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 have in common

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 and the hyperbola (x^(2))/(25)-(y^(2))/(16) =1 have in common

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 and the hyperbola (x^(2))/(25)-(y^(2))/(16) =1 have in common

The slopes of the common tangents of the hyperbolas (x^(2))/(9)-(y^(2))/(16)=1 and (y^(2))/(9)-(x^(2))/(16)=1 , are