A hyperbola, having the transverse axis of the length , is confocal with the ellipse 3x2 + 4y2 = 12. Then, its equation is
None of these
The equation of the ellipse is .
Let e be its eccentricity. Then,
So, coordinates of its foci are (1, 0) and (–1, 0).
Let the equation of the hyperbola be .
It is given that and the hyperbola is confocal to the ellipse.
Hence the equation of the parabola is
If the line y = 2x + λ be a tangent to the hyperbola 36x2 – 25y2 = 3600, then λ is equal to
From any point on the hyperbola tangents are drawn to the hyperbola . The area cut-off by the chord of contact on the asymptotes is equal to
PQ and RS are two perpendicular chords of the rectangular hyperbola xy= c2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CP, CQ, CR and CS equal to
Let be two points on the hyperbola . If (h, k) is the point of intersection of the normal of P and Q, then k is equal to
If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is
If e and e’ be the eccentricities of two conics S = 0 and S’ = 0 and if e2 +e’2 = 3, then both S and S’ can be
If e1 is the eccentricity of the ellipse and e2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e1e2 = 1, then the equation of the parabola, is
The eccentricity of the conjugate hyperbola of the hyperbola x2 – 3y2 = 1 is
The slopes of the common tangents of the hyperbolas and
The locus of point of intersection of tangents at the ends of normal chord of the hyperbola x2 – y2 = a2 is