Hyperbola Test ...

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