Home
Class 12
MATHS
Statement-I A hyperbola whose asymptotes...

Statement-I A hyperbola whose asymptotes include `(pi)/(3)` is said to be equilateral hyperbola.
Statement-II The eccentricity of an equilateral hyperbola is `sqrt(2).`

A

Statement-I is true, Statement-II is also true, Statement-II is the correct explanation of Statement-I.

B

Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement-II is true

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|7 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 10 : Subjective Type Questions|4 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 8 : Matching Type Questions|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

The eccentricity of the hyperbola 4x^(2)-9y^(2)=36 is :

sqrt 2009/3 (x^2-y^2)=1 , then eccentricity of the hyperbola is :

Statement-I (5)/(3) and (5)/(4) are the eccentricities of two conjugate hyperbolas. Statement-II If e_1 and e_2 are the eccentricities of two conjugate hyperbolas, then e_1e_2gt1 .

ABC is a triangle such that angleABC=2angleBAC . If AB is fixed and locus of C is a hyperbola, then the eccentricity of the hyperbola is

Statement-I If eccentricity of a hyperbola is 2, then eccentricity of its conjugate hyperbola is (2)/(sqrt(3)) . Statement-II if e and e_1 are the eccentricities of two conjugate hyperbolas, then ee_1gt1 .

Statement-I A hyperbola and its conjugate hyperbola have the same asymptotes. Statement-II The difference between the second degree curve and pair of asymptotes is constant.

Find the centre, eccentricity, foci and directrices of the hyperbola : x^2-3y^2-2x=8.

Find the standard equation of hyperbola in each of the following cases: (i) Distance between the foci of hyperbola is 16 and its eccentricity is sqrt2. (ii) Vertices of hyperbola are (pm4,0) and foci of hyperbola are (pm6,0) . (iii) Foci of hyperbola are (0,pmsqrt(10)) and it passes through the point (2,3). (iv) Distance of one of the vertices of hyperbola from the foci are 3 and 1.

Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 . The transverse and conjugate axes of this hyperbola coincide with the major and minor axis of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1. Then,

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