Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202125 Feb 2021Evening ShiftMathematicsHyperbolaActual

A hyperbola passes through the foci of the ellipse x 2 25 + y 2 16 = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

Options

  1. Ax 2 9 - y 2 16 = 1
  2. Bx 2 - y 2 = 9
  3. Cx 2 9 - y 2 25 = 1
  4. Dx 2 9 - y 2 4 = 1

Correct answer

A. x 2 9 - y 2 16 = 1

Step-by-step solution

For ellipse e 1 = 1 - b 2 a 2 = 3 5 for hyperbola e 2 = 5 3 Let hyperbola be x 2 a 2 - y 2 b 2 = 1 ∵ it passes through 3 , 0 ⇒ 9 a 2 = 1 ⇒ a 2 = 9 ⇒ b 2 = a 2 e 2 - 1 = 9 25 9 - 1 = 16 ∴ Hyperbola is x 2 9 - y 2 16 = 1 option 1

Practice Hyperbola on Quantrex Academy →

More from Hyperbola

If the eccentricity e of the hyperbola x^2 a^2 - y^2 b^2 = 1 , passing through (6, 4 3 ) , satisfies 15(e^2 + 1) = 34e , then the length of the latus rectum of the hyperbola x^2 b^ 2026Let the eccentricity e of a hyperbola satisfy the equation 6e^2 - 11e + 3 = 0 . If the foci of the hyperbola are (3, 5) and (3, -4) , then the length of its latus rectum is : 2026Let H: x^2 a^2 - y^2 b^2 =1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is 8 3 . If the line x= intersects the hyperbola H 2026Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such that the mid point of the line segment PQ is ( 1 2 , - 1 2 ) . Then the area of the triangl 2026For some (0, 2 ) , let the eccentricity and the length of the latus rectum of the hyperbola x²-y² ² =8 be e₁ and l₁ , respectively, and let the eccentricity and the length of the l 2026Let PQ be a chord of the hyperbola x² 4 - y² b² =1 , perpendicular to the x -axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the eccentricity 2026Let the domain of the function f(x)= ₃ ₅ ₇ (9 x-x²-13 ) be the interval ( m , n ) . Let the hyperbola x² a ² - y² ~b ² =1 have eccentricity n 3 and the length of the latus rectum 8 2026Let P (10,2 15 ) be a point on the hyperbola x² a ² - y² ~b ² =1 , whose foci are S and S ^ . If the length of its latus rectum is 8, then the square of the area of PSS ^ is equal 2026 Full Hyperbola list All JEE Main PYQs