If the eccentricity of the hyperbola `x^2-y^2sec^2alpha=5\ i s\ sqrt(3)` times the eccentricity the ellipse `x^2sec^2alpha+y^2=25\ t h e n\ alpha=` a.`pi/6` b. `pi/4` c. `pi/3` d. `pi/2`

lf the eccentricity of the hyperbola x^2-y^2(sec)^2alpha=5 is sqrt3 times the eccentricity of the ellipse x^2(sec)^2alpha+y^2=25, then a value of alpha is : (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

lf the eccentricity of the hyperbola x^2 - y^2 sec^2 alpha=5 is sqrt3 times the eccentricity of the ellipse x^2 (sec^2alpha )+y^2=25, then a value of alpha is : (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is (a) 2 (b) 2sqrt(3) (c) 4 (d) 4/5

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is (a) 2 (b) 2sqrt(3) (c) 4 (d) 4/5

The eccentricity of the ellipse 4x^2+9y^2+8x+36 y+4=0 is a. 5/6 b. 3/5 c. (sqrt(2))/3 d. (sqrt(5))/3

Equation of the tangent to the hyperbola 4x^(2)-9y^(2)=1 with eccentric angle pi//6 is

The angles at which the circles (x-1)^2+y^2=10a n dx^2+(y-2)^2=5 intersect is pi/6 (b) pi/4 (c) pi/3 (d) pi/2

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

If latus recturn of the ellipse x^2 tan^2 alpha+y^2 sec^2 alpha= 1 is 1/2 then alpha(0 lt alpha lt pi) is equal to

If t a nalpha=x/(x+1)\ a n dtanbeta=1/(2x+1),\ t h e n\ alpha+beta is equal to pi/2 b. pi/3 c. pi/6 d. pi/4