If the foci of the ellipse and the hyperbola conincide, then the value of b2 is
Hence the foci are , i.e.
Now the foci coincide therefore for ellipse
ae = 3 or a2e2 = 9
or a2 – b2 = 9 or 16 – 9 = b2 .
If (asecθ, btanθ) and (asecÏ•, btanÏ•) are the ends of a focal chord of equal to
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
The point of intersection of the curves whose parametric equation are x = t2 + 1, y = 2t and x = 2s, y = 2/s, is given by
The area of triangle formed by the lines x – y = 0, x + y = 0 and any tangent to the hyperbola x2 – y2 = a2 is
A circle cuts the rectangular hyperbola xy = 1 in the points (xr, yr),r = 1, 2, 3, 4. Then the values of x1x2x3x4 and y1y2y3y4 respectively, are
A hyperbola, having the transverse axis of length , is confocal with the ellipse 3x2 + 4y2 = 12. Then its equation is
If e and e’ be the eccentricities of two conics S and S’ such that e2 + e’2 = 3, then both S and S’ are
The eccentricity of the hyperbola 2x2 – y2 = 4 is
Which one of the following is independent of in the hyperbola .
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