Home
Class 12
MATHS
If L is the length of the latus rectum o...

If `L` is the length of the latus rectum of the hyperbola for which `x=3a n dy=2` are the equations of asymptotes and which passes through the point (4, 6), then the value of `L/(sqrt(2))` is_____

Text Solution

Verified by Experts

The correct Answer is:
4
The equation of hyerbola is
`(x-3)(y-2)=c^(2)`
`"or "xy-2x-3y+6=c^(2)`
It passes through (4,6). Then,
`4xx6-2xx4-3xx6+6=c^(2)`
`"or "c=2`
`therefore" Latus rectum"=2sqrt2c=2sqrt2xx2=4sqrt2`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise JEE Main Previous Year|3 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

If L is the length of the latus rectum of the hyperbola for which x=3 and y=2 are the equations of asymptotes and which passes through the point (4,6), then the value of (L)/(sqrt(2)) is

The length of the latus rectum of the hyperbola 3x ^(2) -y ^(2) =4 is

The length of the latus rectum of 3x^(2) - 2y^(2) =6 is

Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 as its asymptotes and which passes through the origin.

The length of the latus rectum of 3x^(2) -4y +6x - 3 = 0 is

If L is the length of the latus rectum of the parabola 289{(x-3)^(2)+(y-1)^(2)}=(15x-8y+13)^(2) then L is equal to

The equation of the hyperbola which passes through thepoint (2,3) and has the asymptotes 4x+3y7=0 and x2y-1=0 is

Find the equation of the hyperbola,whose asymptotes are the straight lines (x+2y+3)=0,(3x+4y+5)=0 and which passes through the point (1-1)

The length of the latus rectum of the ellipse 2x^(2) + 3y^(2) - 4x - 6y - 13 = 0 is