Let a hyperbola has centre at `(0,0)` .A line `x+y=2` touches this hyperbola at P`(1,1)` and intersects the asymptotes at `A` and `B` such that `AB=6sqrt(2)` units.
Angle subtended by `AB` at centre of hyperbola is
A) `sin^(-1)((4)/(5))`, B) `sin^(-1)((2)/(5))`, C) `sin^(-1)((3)/(5))`, D) `tan^(-1)((4)/(3))`

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 line y = 4x + c touches the hyperbola x^(2) - y^(2) = 1 if

The angle between the tangents to the curves y=x^2a n dx=y^2a t(1,1) is cos^(-1)(4/5) (b) sin^(-1)(3/5) tan^(-1)(3/4) (d) tan^(-1)(1/3)

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 pair of asymptotes is

Solve the following equations: sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^(-1)x sin^(-1)6x+sin^(-1)6sqrt(3)x=pi/2

Consider a hyperbola xy = 4 and a line y = 2x = 4 . O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Shortest distance between the line and hyperbola is

The acute angle between the plane 5x-4y+7z=13 and the y-axis is givne by (A) sin^-1(5/sqrt(90)) (B) sin^-1((-4)/sqrt(90)) (C) sin^-1(7/sqrt(90)) (D) sin^-1(4/sqrt(90))

The acute angle between the planes 5x-4y+7z=13 and the y-axis is given by (A) sin^-1(5/sqrt(90)) (B) sin^-1((-4)/sqrt(90)) (C) sin^-1(7/sqrt(90)) (D) sin^-1(4/sqrt(90))

Tangents at any point P is drawn to hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 intersects asymptotes at Q and R, if O is the centre of hyperbola then

If A = 2 tan^(-1) (2 sqrt2 -1) and B = 3 sin^(-1) ((1)/(3)) + sin^(-1) ((3)/(5)) , then which is greater ?