Home
Class 12
MATHS
If e is the eccentricity of the hyperbol...

If e is the eccentricity of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` and `theta` is the angle between the asymptotes, then `cos.(theta)/(2)` is equal to

A

`(1-e)/(e)`

B

`(2)/(e ) -e`

C

`(1)/(e )`

D

`(2)/(e )`

Text Solution

Verified by Experts

The correct Answer is:
C
`theta = 2 tan^(-1).(b)/(a) rArr tan.(theta)/(2) = (b)/(a)`
`rArr cos.(theta)/(2) = (a)/(sqrt(a^(2)+b^(2))) = (1)/(sqrt(1+(b^(2))/(a^(2)))) = (1)/(e)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The eccentricity of the hyperbola (y^(2))/(9)-(x^(2))/(25)=1 is …………………

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

Find the angle between the asymptotes of the hyperbola (x^2)/(16)-(y^2)/9=1 .

If eccentricity of the hyperbola (x^(2))/(cos^(2) theta)-(y^(2))/(sin^(2) theta)=1 is move than 2 when theta in (0,(pi)/2) . Find the possible values of length of latus rectum (a) (3,oo) (b) 1,3//2) (c) (2,3) (d) (-3,-2)

The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+(y+1)^2)|=1 is ______

If e_(1) is the eccentricity of the ellipse (x^(2))/(25)+(y^(2))/9=1 and if e_(2) is the eccentricity of the hyperbola 9x^(2)-16y^(2)=144 , then e_(1)e_(2) is. . . . .

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.