Hyperbola - 1 - JEE MCQ

A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x² + 4y² = 12. Then its equation is:

The number of tangents and normals to the hyperbola  of the slope 1 is

If (4, 0) and (–4, 0) be the vertices and (6, 0) and (–6, 0) be the foci of a hyperbola, then its eccentricity is-

If centre, vertex & focus of hyperbola are (2, 0) (4, 0) & (8, 0) then length of latus rectum

Consider the set of hyperbola xy = k, k ∈ R. Let e₁ and e₂ be the eccentricities when k = 16 and k = 25 respectively then the value of e₁² – e₂² equals -

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. then CP² + CQ² + CR² + CS² is equal to -

PM and PN are the perpendiculars from any point on a rectangular hyperbola to its asymptotes. If Q divides MN in the ratio 3 : 1, then the locus of Q is -

A common tangent to 9x² – 16y² = 144 and x² + y² = 9 is -

From any point on a hyperbola xy = c² tangents are drawn to another hyperbola xy = a² which has the same asymptotes. Then the chord of contact cuts off a constant area from the asymptotes:

A point P moves in such a way that the sum of the slopes of the normals drawn from itto the hyperbola xy = 4 is equal to the sum of the ordinates of feet of the normals. The locus of P is a parabola x² = 4y. Then the least distance of this parabola from the circle x² – y² – 24x + 128 = 0 is -

Let ax + by = 1 be a chord of the curve 3x² – y² – 2x + 4y = 0 intersecting the curve at the points A and B such that AB subtends a right angle at the origin O. If the triangle OAB is isosceles then the area of Δ cannot exceed

The distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ is-

If xy = m² – 9 be a rectangular hyperbola whose branches lie only in the second and fourth quadrant, then -

The product of the lengths of perpendiculars drawn from any point on the hyperbola x² – 2y² – 2 = 0 to its asymptotes, is -

Conjugate hyperbola of hyperbola 2x² – 3y² = – 6 is :