Home
Class 12
MATHS
The line 2x+y=1 is tangent to the hyperb...

The line `2x+y=1` is tangent to the hyperbla `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`. If this line passes through the point of intersection of the nearest directrix and the `x`-axis, then the eccentricity of the hyperbola is

A

`(3)/(2)`

B

2

C

`(5)/(2)`

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE HYPERBOLA

    ML KHANNA|Exercise MISCELLANGEOUS EXERCISE (MATCHING ENTERIES) |1 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise SELF ASSESSMENT TEST|9 Videos

  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos

Similar Questions

Explore conceptually related problems

The line 2x+y=1 is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If this line passes through the point of intersection of the nearest directrix and the x-axis,then the eccentricity of the hyperbola is

Let P(6,3) be a point on the hyperbola parabola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

Knowledge Check

  • The line 2x + y = 1 touches a hyperbola and passes through the point of intersection of a directrix and the x-axis. The equation of the hyperbola is

    A
    `(x^(2))/(1)-(y^(2))/(3)=1`
    B
    `(x^(2))/(1)-(y^(2))/(3)=2`
    C
    `(x^(2))/(3)-(y^(2))/(1)=1`
    D
    `(x^(2))/(3)-(y^(2))/(1)=2`

  • Let P(6,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at the point P intersects the x-axis at (9,0) then the eccentricity of the hyperbola is

    A
    `sqrt((5)/(2))`
    B
    `sqrt((3)/(2))`
    C
    `sqrt(2)`
    D
    `sqrt(3)`

  • If the line ky=x+1 passes through the point on intersection of the two lines 2x-3y+5=0 and 3x+2y+1=0, then :k=

    A
    -1
    B
    0
    C
    1
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    The tangent at a point P on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the point (0,-b) and the normal at P passes through the point (2a sqrt(2),0). Then the eccentricity of the hyperbola is 2( b) sqrt(2)(c)3(d)sqrt(3)

    If a line passes through the point of intersection of the lines 2x+y=5,x-y=1 and having slope 2 then it also passes through the point

    Show that the line y=2x-4 is a tangent to the hyperbola (x^(2))/(16)-(y^(2))/(48)=1. Find its point of contact.

    P (6,3) is a point on the hyperbola (x ^(2))/( a ^(2)) - (y ^(2))/( b ^(2)) =1. If the normal at point P intersect the x-axis at (10,0) , then the eccentricity of the hyperbola is

    The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

    Home
    Profile