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Question From class 12 Chapter RELATIONS AND FUNCTIONS

# AB is double ordinate of the hyperbola such that (where 'O' is the origin) is an equilateral triangle, then the eccentricity e of hyperbola satisfies:

Solution :

With the given details. we can draw a hyperbola.<br> Please refer to video for the diagram.<br> Now, coordinates of point are .<br> As angle <br> Slope <br> <br> <br> Now, we know,<br> Eccentricity, <br> <br> As maximum value of is ,<br> So, minimum value of .<br> .<br> <br> So, option is the correct option.

If is a double ordinate of the hyperbola such that is an equilateral triangle, being the center of the hyperbola, then find the range of the eccentricity of the hyperbola.
4:40
Show that the acute angle between the asymptotes of the hyperbola is where is the eccentricity of the hyperbola.
8:01
let the eccentricity of the hyperbola be reciprocal to that of the ellipse if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is (b) a focus of the hyperbola is (c) the eccentricity of the hyperbola is (d) the equation of the hyperbola is
4:45
The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola is equal to (where e is the eccentricity of the hyperbola)
1:54
If normal to hyperbola drawn at an extremity of its latus-rectum has slope equal to the slope of line which meets hyperbola only once, then the eccentricity of hyperbola is
5:28
The eccentricity of the hyperbola is given by
1:23
If the eccentricity of a hyperbola is 2, then find the eccentricity of its conjugate hyperbola.
1:19
If hyperbola passes through the focus of ellipse , then find the eccentricity of hyperbola.
7:00
If the line joining the foci of the hyperbola does not subtend a right angle at any point on the hyperbola whose eccentricity is e, then
2:20
The eccentricity of the hyperbola be reciprocal to that of the ellipse . If the hyperbola passes through a focus of the ellipse, then :
The distance between the foci of a hyperbola is 16 and its eccentricity is then equation of the hyperbola is a. b. c. d.
2:25
If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola ,then find the eccentricity of the hyperbola.
5:36
The eccentricity of the hyperbola is
1:25
The eccentricity of the hyperbola , is
1:31

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FAQs on Relations And Functions
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