Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20252 Apr 2025Morning ShiftMathematicsHyperbolaActual

Let one focus of the hyperbola H : x ^2 a ^2 - y ^2 ~b ^2 =1 be at ( 10 , 0) and the corresponding directrix be x = 9 10 . If e and l respectively are the eccentricity and the length of the latus rectum of H , then 9 ( e ^2+l ) is equal to:

Options

  1. A14
  2. B15
  3. C16
  4. D12

Correct answer

C. 16

Step-by-step solution

aligned & ae = 10 and a e = 9 10 & a ^2=9 and e = 10 3 & Now aligned & ( ae )^2= a ^2+ b ^2 & 10=9+ b ^2 ~b ^2=1 & & = 2 ~b ^2 a = 2(1) 3 & 9 ( e ^2+ ) & =9 ( 10 9 + 2 3 ) & =10+6 & =16 aligned aligned

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