Find The Equations Of Tangents To The Hyperbola x2 – 4y = 36 Which Are Perpendicular To The Line x – Y + 4 = 0

 touches the hyperbola x² – 2y² = 4, then the point of contact is

Equation of tangent to the hyperbola 2x² – 3y² = 6 which is parallel to the line y = 3x + 4 is

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

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

Let two perpendicular chords of the ellipse  each passing through exactly one of the foci meet at a point P. If from P two tangents are drawn to the hyperbola , then 

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

Find the coordinates of foci, the eccentricity and latus rectum. Determine also the equation of its directrices for the hyperbola

4x² – 9y² =36.

Find the distance from A(4, 2) to the points in which the line 3x – 5y = 2 meets the hyperbola xy = 24. Are these points on the same side of A?

The asymptotes of the hyperbola  makes an angle 60⁰ with x-axis. Write down the equation of determiner conjugate to the diameter y = 2x.

Two straight lines pass through the fixed points  and have gradients whose product is k > 0. Show that the locus of the points of intersection of the lines is a hyperbola.