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?

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 equations of tangents to the hyperbola x² – 4y = 36 which are perpendicular to the line x – y + 4 = 0

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

4x² – 9y² =36.

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.

Find the equation of the triangles drawn from the point (–2, –1) to the hyperbola 2x² – 3y² = 6.