lf the eccentricity of the hyperbola x^...

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`

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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

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

if 2sec2alpha=tan beta+cot beta then one of the value of alpha+beta is (A) pi (B) npi- pi/4, n in ZZ (C) pi/4 (D) pi/2

The angle of intersection of the parabola y^2=4\ a x and x^2=4a y at the origin is (a) pi//6 (b) pi//3 (c) pi//2 (d) pi//4

If the eccentricity of the hyperbola (x^(2))/((1+sin theta)^(2))-(y^(2))/(cos^(2)theta)=1 is (2)/(sqrt3) , then the sum of all the possible values of theta is (where, theta in (0, pi) )

If (sqrt(3))b x+a y=2a b touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the eccentric angle of the point of contact is pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]] , then A+A^(prime)=I , if the value of alpha is (A) pi/6 (b) pi/3 (c) pi (d) (3pi)/2

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 the line xcostheta=2 is the equation of a transverse common tangent to the circles x^2+y^2=4 and x^2+y^2-6sqrt(3)x-6y+20=0 , then the value of theta is (5pi)/6 (b) (2pi)/3 (c) pi/3 (d) pi/6

The angle of intersection of the curves y=2\ sin^2x and y=cos2\ x at x=pi/6 is (a) pi//4 (b) pi//2 (c) pi//3 (d) pi//6

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