Question

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

Solution

Correct option is

1,1

 circle is xy2 + 2gx + 2fy + k = 0 solving we get

t4 + 2gt3 + kt+ 2ft + 1 = 0 

SIMILAR QUESTIONS

Q1

If (asecθ, btanθ) and (asecÏ•, btanÏ•) are the ends of a focal chord of  equal to

 

Q2

The equation of a line passing through the center of a rectangular hyperbola is x – y – 1 = 0, if one of its asymptotes is 3x – 4y – 6 = 0, the equation of the other asymptote is

 

Q3

The point of intersection of the curves whose parametric equation are x = t2 + 1, y = 2t and x = 2sy = 2/s, is given by

Q4

The area of triangle formed by the lines x – y = 0, x + y = 0 and any tangent to the hyperbola x – y= ais

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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