Equation of the hyperbola. `2b=5` and point `(1,-2)`

Find the equation of the hyperbola passing through the points (2, 1) and (4, 3).

Find the equation of hyperbola with foci at the points (-3,5) and (5,5) and length of latus rectum =2sqrt(8) units.

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the tangent to the hyperbola at (-1, 7/2) is

The equation of the tangent to the hyperbola 4y^(2)=x^(2)-1 at the point (1,0) , is

The equation of the tangent to the hyperbola 4y^(2)=x^(2)-1 at the point (1,0) , is

One focus of a hyperbola is located at the point (1,-3) and the corresponding directrix is the line y=2. Find the equation of the hyperbola if its eccentricty is (3)/(2) .

One focus of a hyperbola is located at the point (1, -3) and the corresponding directrix is the line y = 2. Find the equation of the hyperbola if its eccentricity is (3)/(2)

Find the equation of normal to the hyperbola 4x^(2)-9y^(2)=36 , at the point (1,2)