The Angle Between The Asymptotes Of The Hyperbola  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 equation of the conic with focus at (1, –1), directrix along x – y + 1 = 0 and with eccentricity  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

The curve for which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is