Home
Class 11
MATHS
Find the equations of the hyperbola sati...

Find the equations of the hyperbola satisfying the given conditions :Foci `(+-5,0)`, the transverse axis is of length 8.

Text Solution

Verified by Experts

Here, `2a=8rArra=4`
and `ae=5rArre=(5)/(4)`
`"Now", b^(2)=a^(2)(e^(2)-1)`
`=16((25)/(16)-1)=9`
Therefore, equation of hyperbola
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1rArr(x^(2))/(16)-(y^(2))/(9)=1`
`rArr9x^(2)-16y^(2)=144`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|8 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11.3|20 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|20 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|6 Videos

Similar Questions

Explore conceptually related problems

Find the equations of the hyperbola satisfying the given conditions :Foci (0,+-13) , the conjugate axis is of length 24.

Find the equations of the hyperbola satisfying the given conditions :Foci (+-3sqrt(5),0) , the latus rectum is of length 8.

Find the equations of the hyperbola satisfying the given conditions :Foci (+-4,0) , the latus rectum is of length 12

In each of the following find the equations of the hyperbola satisfying he given condition: foci (+-5,0) transverse axis =8

Find the equations of the hyperbola satisfying the given conditions :Vertices (+-7,0) , e=4/3

Find the equation for the ellipse that satisfies the given conditions:Foci (+-3,0),a=4

Find the equation of the ellipse that satisfies the given conditions: Foci (pm3,0),a=4

Find the equations of the hyperbola satisfying the given conditions :Foci (0,+-sqrt(10)) , passing through (2,3)

Find the equations of the hyperbola satisfying the given conditions :Vertices (0,+-5),f o c i (0,+-8)

In each of the following find the equations of the hyperbola satisfying the given condition: foc i\ (+-3sqrt(5),0) , the latus rectum =8