Hyperbola - 2 - JEE MCQ

The coordinates of the point of intersection of two tangents to a rectangular hyperbola referred to its asymptote as axes are -

If the sum of the squares of slopes of the normals from a point P to the hyperbola xy = c² is equal to λ (λ ∈ R⁺), then the locus of the point P is–

The equation of the hyperbola in the standard form (with transverse axis along the x-axis) having the length of the latus rectum = 9 unit and eccentricity = 5/4 , is - 

If the normal at P to the rectangular hyperbola x² – y² = 4 meets the axis in G and g and C is the centre of the hyperbola, then -

Equation of a common tangent to the curves y² = 8x and xy = – 1 is

If e and e´ are the eccentricities of the ellipse 5x² + 9y² = 45 and the hyperbola 5x² – 4y² = 45 respectively, then ee´ =

Equation of the chord of the hyperbola 25x² – 16y² = 400 which is bisected at the point (6, 2), is -

Equation of hyperbola passing through origin and whose asymptotes are 3x + 4y = 5 and 4x + 3y = 5, is -

If the tangent and the normal to a rectangular hyperbola at a point cut off intercepts a₁, a₂ on one axis and b₁, b₂ the other axis then a₁a₂ + b₁b₂ is equal to-

The angle between the tangents from (–2, –1) to the hyperbola 2x² – 3y² = 6 is-

At the point of intersection of the rectangular hyperbola xy = c² and the parabola y² = 4ax tangents to the rectangular hyperbola and the parabola make an angle θ and ϕ respectively with x- axis, then–

If P is a point on the hyperbola 16x² – 9y² = 144 whose foci are S₁ and S₂, then PS₁ ~ PS₂ =

Tangents PA and PB are drawn to circle (x + 4)² + (y – 4)² =1 from variable points P on xy = 1. The locus of circumcentre of the triangle PAB is:

If equation (10x – 5)² + (10y – 4)² = λ² (3x + 4y – 1)² represents a hyperbola, then -