If `(x+1)/(x-1)=a/b` and `(1-y)/(1+y)=b/a` , then the value of `(x-y)/(1+x y)` is `(2a b)/(a^2-b^2)` (b) `(a^2-b^2)/(2a b)` (c) `(a^2+b^2)/(2a b)` (d) `(a^2-b^2\ )/(a b)`

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

If (x)/(a)-(y)/(b) tan theta =1 and (x)/(a) tan theta +(y)/(b)=1 , then the value of (x^(2))/(a^(2))+(y^(2))/(b^(2)) is

If a , b >0 , then minimum value of y=(b^2)/(a-x)+(a^2)/x in (0,a) is (a) (a+b)/a (b) (a b)/(a+b) (c) 1/a+1/b (d) ((a+b)^2)/a

If x=(a+b)/(a-b),y=(b+c)/(b-c),z=(c+a)/(c-a) then the value of ((2x+2)(4y+4)(z+1))/((x-1)(y-1)(z-1)) is equal to

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A)(a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B)(a+b)(x^2+y^2)=2a b (C)(x^2+y^2)=(a^2+b^2) (D)(a-b)^2(x^2+y^2)=a^2b^2

Area of the quadrilateral formed with the foci of the hyperbola x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1 (a) 4(a^2+b^2) (b) 2(a^2+b^2) (c) (a^2+b^2) (d) 1/2(a^2+b^2)

Area of the quadrilateral formed with the foci of the hyperbola x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1 (a) 4(a^2+b^2) (b) 2(a^2+b^2) (c) (a^2+b^2) (d) 1/2(a^2+b^2)

Show that the tangent of an angle between the lines x/a+y/b=1 and x/a-y/b=1\ i s(2a b)/(a^2-b^2)

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A) (a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B) (a+b)(x^2+y^2)=2a b (C) (x^2+y^2)=(a^2+b^2) (D) (a-b)^2(x^2+y^2)=a^2b^2

If the origin is shifted to the point ((a b)/(a-b),0) without rotation, then the equation (a-b)(x^2+y^2)-2a b x=0 becomes (A) (a-b)(x^2+y^2)-(a+b)x y+a b x=a^2 (B) (a+b)(x^2+y^2)=2a b (C) (x^2+y^2)=(a^2+b^2) (D) (a-b)^2(x^2+y^2)=a^2b^2