Question

Consider a branch of the hyperbola  with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is

Solution

Correct option is

The given equation can be written as

            

or       

Above represents a hyperbola   

Where   

Vertex A = (a, 0), = (ae, 0)

and   

  

      

                                                                                                                      

 

SIMILAR QUESTIONS

Q1

A circle cuts the rectangular hyperbola xy = 1 in the points (xr, yr),r = 1, 2, 3, 4. Then the values of x1x2x3x4 and y12y3y4 respectively, are

Q2

A hyperbola, having the transverse axis of length , is confocal with the ellipse 3x2 + 4y2 = 12. Then its equation is

Q3

If and e’ be the eccentricities of two conics S and S’ such that e2 + e2 = 3, then both S and S’ are

Q4

The eccentricity of the hyperbola 2x2 – y2 = 4 is

Q5

If the foci of the ellipse  and the hyperbola  conincide, then the value of b2 is

Q6

Which one of the following is independent of  in the hyperbola .

Q7

 touches the hyperbola x2 – 2y2 = 4, then the point of contact is

Q8

Equation of tangent to the hyperbola 2x2 – 3y2 = 6 which is parallel to the line y = 3x + 4 is

Q9

Let be two points on the hyperbola . If (h, k) is thepoint of intersection of the normal’s at P and Qk is equal to

Q10

Let be two points on the hyperbola . If (h, k) is thepoint of intersection of the normal’s at P and Qk is equal to