Nomenclature of ellipse and hyperbola

Nomenclature 2

Tangents of ellipse and hyperbola

Normal to ellipse and hyperbola

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Foci of the ellipse are (A) (+- 4, 0) (B) (+-3, 0) (C) (+-5, 0) (D) none of these

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. If l and l\' be the length of semi latera recta of ellipse and hyperbola, then ll\'= (A) 144/15 (B) 256/15 (C) 225/12 (D) none of these

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(A^(2))-(y^(2))/(B^(2))=1 are given to be confocal and length of mirror axis of the ellipse is same as the conjugate axis of the hyperbola. If e_1 and e_2 represents the eccentricities of ellipse and hyperbola respectively, then the value of e_(1)^(-2)+e_(1)^(-2) is

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Equation of ellipse is : (A) x^2/16 + y^2/9 =1 (B) x^2/25 + y^2/9 = 1 (C) x^2/25 + y^2/16 = 1 (D) none of these

The ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 and hyperbola x^(2)/A^(2) - y^(2)/B^(2) = 1 are given to be confocal and length of minor axis is of ellipse is same as the conjugate axis of the hyperbola . If e_(1)" and " e_(2) are the eccentricity of ellipse and hyperbola then value of 1/((e_(1))^(2)) + 1/((e_(2))^(2)) is ______

Problems based on Tangent to ellipse and hyperbola