The asymptote of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` form with any tangent to the hyperbola a triangle whose area is `a^(2) tan lambda` in magnitude then find its eccentricity.

The asymptote of the hyperbola x^2/a^2+y^2/b^2=1 form with ans tangen to the hyperbola triangle whose area is a^2 tan lambda in magnitude then its eccentricity is: (a) sec lambda (b) cosec lambda (c) sec^2 lambda (d) cosec^2 lambda

The eccentricity of the hyperbola (y^(2))/(9)-(x^(2))/(25)=1 is …………………

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

A tangent is drawn at any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 . If this tangent is intersected by the tangents at the vertices at points P and Q, then which of the following is/are true

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)).

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot