If `x^2+y^2=x^2y^2` then find the range of `(5x+12 y+7x y)/(x y)` .

If x^(2)+y^(2)+6x-4y-12=0 then find the ragne of 2x+y

For all, x ,y in Rdot find the range of ((x+y)(1-x y))/((1+x^2)(1+y^2)) .

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2))

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

If R={(x,y): x,y in W, x ^(2)+y^(2)=25} , then find the domain and range or R.

If (x^(2))/(144)-(y^(2))/(25)=1 . Find the range of (144)/(x)+(25)/(y) .

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.