The ellipse x² 25 + y² 16 =1 and the hyperbola x² 25 - y² 16 =1 have in common

Step-by-step solution

Equation of ellipse is x² 25 + y² 16 =1, a>b and equation of hyperbola is x² 25 - y² 16 =1, a>b Let e and e^ be the eccentricities of the ellipse and hyperbola. So, e= a²-b² a² = 25-16 25 = 3 5 and e^ = a²+b² a² = 25+16 25 = 41 5 (i) Centre of ellipse (0,0) and centre of hyperbola is (0,0) (ii) Foci of ellipse are ( a e, 0) or ( 3,0) . Foci of hyperbola are ( a e^ , o ) or ( 41 , 0) . (iii) Direction of ellipse are x= a e x= 25 3 and directrices of hyperbola are x= a e x= 25 41 (iv) Vertices of ellipse are ( a, 0)