If `(x-(1)/(x))^(2)=x^(2)+y+(1)/(x^(2)),` then the value of y is

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the value of (1)/(y_(1))+(1)/(y_(2)) is

Let x+(1)/(x)=2, y+(1)/(y)=-2 and sin^(-1)x+cos^(-1)y=m pi , then the value of m is

The ordered pair (x,y) satisfying the equation x^(2)=1+6 log_(4)y and y^(2)=2^(x)y+2^(2x+1) and (x_(1), y_(1)) and (x_(2), y_(2)) , then find the value of log_(2)|x_(1)x_(2)y_(1)y_(2)| .

The ordered pair (x,y) satisfying the equation x^(2)=1+6 log_(4)y and y^(2)=2^(x)y+2^(2x+1) and (x_(1), y_(1)) and (x_(2), y_(2)) , then find the value of log_(2)|x_(1)x_(2)y_(1)y_(2)| .

If sin^(2)theta=(x^(2)+y^(2)+1)/(2x) . Find the value of x and y.

If (1)/(8)x+(1)/(8)y=y-2x , then what is the value of (x)/(y) ?

If t(1+x^2)=x and x^2+t^2=y, then at x=2 the value of (d y)/(d x) is equal to

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

If 2^(x+y) = 6^(y) and 3^(x-1) = 2^(y+1) , then the value of (log 3 - log 2)//(x-y) is

If x and y are real numbers such that 16^(x^(2)+y)+16^(x+y^2)=1 , then find the values of x and y.