Tangent are drawn to the hyperbola `(x^(2))/(9)-(y^(2))/(4)=1` parallel to the straight line `2x-y=1.` The points of contact of the tangents on the hyperbola are

Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the sraight line 2x-y=1. The points of contact of the tangents on the hyperbola are (A) (9/(2sqrt2),1/sqrt2) (B) (-9/(2sqrt2),-1/sqrt2) (C) (3sqrt3,-2sqrt2) (D) (-3sqrt3,2sqrt2)

The equation of a tangent to the hyperbola 3x^(2)-y^(2)=3 , parallel to the line y = 2x +4 is

The equation of a tangent to the hyperbola x^(2)-2y^(2)=2 parallel to the line 2x-2y+5=0 is-

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola. (a) Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

Find the points on the hyperbola 2x^(2)-3y^(2)=6 at which the slop of the tangent line is (-1)

From the point (2, 2) tangent are drawn to the hyperbola (x^2)/(16)-(y^2)/9=1. Then the point of contact lies in the (a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

From any point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=2. The area cut-off by the chord of contact on the asymptotes is equal to: (a) a/2 (b) a b (c) 2a b (d) 4a b

Tangents are drawn to the hyperbola 3x^2-2y^2=25 from the point (0,5/2)dot Find their equations.