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 any tangent to the hyperbola a triangle whose area is a^2 tanlambda in magnitude, then its eccentricity is

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}

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}

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}

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

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if (a) lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=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=2 x + lambda be a tangent to the hyperbola 36 x^(2)-25 y^(2)=3600 then lambda=

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