An ellipse `(x^(2))/(4)+(y^(2))/(3)=1` is confocal with the hyperbola `(x^(2))/(cos^(2)theta)-(y^(2))/(sin^(2)theta)=1` then the set of values of `theta` is

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 the tangent at the point (2sec theta,3tan theta) of the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 then the value of theta

If x= 2sin^(2)theta and y= 2cos^(2)theta+ 1 then the value of x+ y is

If x=a sin theta and y=b cos theta , then prove : (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If cos^(-1)x+cos^(-1)y=theta show that x^(2)-2xy cos theta+y^(2)=sin^(2)theta

If the eccentricity of the hyperbola x^(2)-y^(2)sec^(2)theta=4 is sqrt3 times the eccentricity of the ellipse x^(2)sec^(2)theta+y^(2)=16 , then the value of theta equals

If sin theta=(x^2-y^2)/(x^2+y^2) then find the values of cos theta and cot theta

If the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, is normal at (a cos theta,b sin theta) then eccentricity of the ellipse is

If cos^(-1)((x)/(2))+cos^(-1)((y)/(3))=theta, prove that 9x^(2)-12xy cos theta+4y^(2)=36sin^(2)theta