Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202123 Aug 2021Evening ShiftMathematicsHyperbolaActual

In a hyperbola, if the length of transverse axis is twice that of the conjugate axis, then the distance between its directrices is..... units.

Options

  1. A8 b 5
  2. B8 a 5
  3. C2 a 5
  4. D2 b 5

Correct answer

A. 8 b 5

Step-by-step solution

Given, in a hyperbola, the length of transverse axis is twice that of the conjugate axis. The equation of standard hyperbola is x^2 a^2 - y^2 b^2 =1 Length of transverse axis =2 length of conjugate axis 2 a=2 2 b array lll & a & =2 b & b^2 & =a^2 (e^2-1 ) array array ll & a^2 4 =a^2 (e^2-1 ) & e^2=1+ 1 4 = 5 4 array e= 5 2 Distance between its directrix = 2 a e = 2(2 b) 5 / 2 = 8 b 5

Practice Hyperbola on Quantrex Academy →

More from Hyperbola

The difference between the distance of any point on the hyperbola from the two foci is 16 and the eccentricity is 2 . Then the equation of the hyperbola is 2026In the figure Statement-I: When > 0 , the section is hyperbola Statement-II: When > 90^ , the section is ellipse Which of the following is correct? 2026If the line y = 2x + is a tangent to the hyperbola 36x^2 - 25y^2 = 3600 , then = 2026If the line 4x + 3y = 7 touches the hyperbola x^2 - y^2 = 7 , then the sum of the co-ordinates of the point of contact is... 2026If the eccentricity of the hyperbola x^2 a^2 - y^2 b^2 =1 passing through the point (4,6) is 2, then the equation of the tangent to this hyperbola at (4,6) is 2025A hyperbola passes through the point P ( 2 , 3 ) and has foci at ( 2,0) . Then the point that lies on the tangent drawn to this hyperbola at P is 2025If is the angle subtended by a latus rectum at the centre of the hyperbola having eccentricity 2 7 - 3 , then = 2025The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola x^2 4 - y^2 5 =1 meets the x -axis and y -axis at A and B respectively. If O is the origi 2025 Full Hyperbola list All AP EAMCET PYQs