The Equation Of The Conic With Focus At (1, –1), Directrix Along x – y + 1 = 0 And With Eccentricity  is

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Let P and , where , be two points on the hyperbola . If (h, k) is the point of intersection of the normal’s at P and Q, then k is equal to

If x = 9 is the chord of contact of the hyperbola x² – y² = 9, then equation of corresponding of tangents is

The locus of the mid-point of the chord of the circle x² + y² = 16, which are tangent to the hyperbola 9x² – 16y² = 144 is

The angle between lines joining origin to the points of intersection of the line  and the curve y² – x² = 4 is

If a circle cuts a rectangular hyperbola xy = c² in A, B, C, D and the parameters of these four points be t₁, t₂, t₃ and t₄ respectively. Then

The locus of the middle point of the chords of hyperbola 3x² – 2y² + 4x – 6y = 0 parallel to y = 2x is

The angle between the asymptotes of the hyperbola  is

If P is any point on the hyperbola , and S₁ and S₂ are its foci, then | S₁P – S₂P | =

The point of intersection of two perpendicular tangents to  lies on the circle