Home
Class 11
MATHS
Find the coordinates of the foci, the ve...

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the Hyperbola `49y^(2)-16x^(2)=784`

Text Solution

Verified by Experts

Equation of hyperbola
`49y^(2)-16x^(2)=784`
`rArr" "(y^(2))/(16)-(x^(2))/(49)=1`
The transverse axis of hyperbola is along y-axis.
Comparing with `(y^(2))/(b^(2))-(x^(2))/(a^(2))=1`
`b^(2)=16," "a^(2)=49`
`rArrb=4," "a=7`
`:. "Vertices"-=(0,pmb)-=(0,pm4)`
Eccentricity `e=sqrt(1+(a^(2))/(b^(2)))`
`=sqrt(1+(49)/(16))=sqrt((65)/16)=sqrt((65)/4)`
Now, `be4xx=(sqrt(65))/(4)=sqrt(65)`
`:. "Coordinates of foci"-=(0,pmbe)-=(0,pmsqrt(65))`
Length of latus latus rectum `=(2a^(2))/(b)=(2xx49)/(4)=(49)/(2)`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|8 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Exercise 11.3|20 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|20 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|6 Videos

Similar Questions

Explore conceptually related problems

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the Hyperbola 9y^(2)-4x^(2)=36

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the Hyperbola 16x^(2)-9y^(2)=576

Find the coordinates of the foci and the vertices,the eccentricity and the length of the latus rectum of the hyperbolas.49y^(2)-16x^(2)=7284

Find the coordinates of the foci and the vertices,the eccentricity and the length of the latus rectum of the hyperbolas.5y^(2)-9x^(2)=36

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the Hyperbola (y^(2))/(9)-(x^(2))/(27)=1

Find the co-ordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola y^(2) - 25x^(2) = 25 .

Find the coordinates of the foci and the vertices,the eccentricity and the length of the latus rectum of the hyperbolas.quad 9y^(2)-4x^(2)=36

Find the coordinates of the foci and the vertices,the eccentricity and the length of the latus rectum of the hyperbolas.16x^(2)-9y^(2)=576

Find the coordinates of the foci and the vertices,the eccentricity and the length of the latus rectum of the hyperbolas.(y^(2))/(9)-(x^(2))/(27)=1