Test: Hyperbola- 2 - JEE MCQ

If x = 9 is the chord of contact of the hyperbola x² - y² = 9, then the equation of the tangent at one of the points of contact is 

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

The mid-point of the chord 4x – 3y = 5 of the hyperbola 2x² - 3y² = 12 is

The equation of the transverse and conjugate axes of a hyperbola are respectively x + 2y – 3 = 0, 2x – y + 4 = 0 and their respective lengths are √2 and 2/√3. The equation of the hyperbola is

If two distinct tangents can be drawn from the point (α,2) on different branches of the hyperbola 

A hyperbola has centre C and one focus at P(6, 8). If its two directrices are 3x + 4y + 10 = 0 and 3x + 4y -10 = 0 then CP =

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

Consider a branch of the hyperbola x² - 2y² - 2y - 6 = 0 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 

If α + β = 3π then the chord joining the points 'a' and 'b' for hyperbola passes through 

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

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

If the line ax + by + c = 0 is a normal to the hyperbola x y = 1, then

A tangent to the parabola x² = 4ay meets the hyperbola x² - y² = a² at two points P and Q, then midpoint of P and Q lies on the curve

The point of intersection of two tangents to the hyperbola x²/a² – y²/b² = 1, the product of whose slopes is c², lies on the curve.

Let P(a secθ, b tanθ) and Q(a secφ, b tanφ) where θ+φ = π/2, be two points on the hyperbola If (h, k) is the point of the intersection of the normals at P and Q, then k is equal to

Foot of normals drawn from the point p(h,k) to the hyperbola  will always lie on the conic

A variable chord PQ, x cos θ + y sin θ = P of the hyperbola  subtends a right angle at the origin. This chord will always touch a circle whose radius is 

If the equation 4x² + ky² = 18 represents a rectangular hyperbola, then k =

The locus of the point of intersection of tangents drawn at the extremities of normal chords to hyperbola xy = c²

The asymptotes of the hyperbola hx + ky = xy are

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

Tangents are drawn to 3x² - 2y² = 6 from a point P. If these tangents intersects the coordinate axes at concyclic points, The locus of P is

If the curve  cut each other orthogonally then 

Let a and b be non–zero real numbers. Then, the equation (ax² + by² + (C) (x² – 5xy + 6y²) = 0 represents 

The asymptotes of the curve 2x² + 5xy + 2y² + 4x + 5y = 0 are given by

A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis is

If the vertex of a hyperbola bisects the distance between its centere and the corresponding focus, then ratio of square of its conjugate axis of the square of its transverse axis is