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 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)cos ec lambda(c)sec^(2)lambda(d)cos ec^(2)lambda

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}

If the sum of the slopes of the normal from a a point P to the hyperbola xy=c^(2) is equal to lambda(lambda in R^(+)), then the locus of point P is (a) x^(2)=lambda c^(2)( b) y^(2)=lambda c^(2)( c) xy=lambda c^(2)( d) none of these

If the line y=2x+lambda be a tangent to the hyperbola 36x^(2)-25y^(2)=3600 , then lambda is equal to

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

P is any point on the hyperbola x^(2)-y^(2)=a^(2) . If F_1 and F_2 are the foci of the hyperbola and PF_1*PF_2=lambda(OP)^(2) . Where O is the origin, then lambda is equal to

If the line y=3x+lambda touches the hyperbola 9x^(2)-5y^(2)=45 , then the value of lambda is

If in any triangle, the area DeltaABC le(b^(2)+c^(2))/(lambda) , then the largest possible numerical value of lambda is

Let a,b,c be the sides of a triangle. No two of them are equal and lambda in R If the roots of the equation x^2+2(a+b+c)x+3lambda(ab+bc+ca)=0 are real, then (a) lambda 5/3 (c) lambda in (1/5,5/3) (d) lambda in (4/3,5/3)