if `y^(2)(y^(2)-6)+x^(2)-8x+24=0`, then maximum value of `sqrt(y^(4)+x^(2))` is

If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(2) + y^(4) is m and maximum value is M, then find the value of M-2m.

If (x,y) lies on the ellipse x^(2)+2y^(3) = 2 , then maximum value of x^(2)+y^(2)+ sqrt(2)xy - 1 is

If x^(2)-6x-27=0 and y^(2)-6y-40=0 , what is the maximum value of x+y ?

If x^2+y^2=4 then find the maximum value of (x^3+y^3)/(x+y)

Suppose xa n dy are real numbers and that x^2+9y^2-4x+6y+4=0 . Then the maximum value of ((4x-9y))/2 is__________

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

If (x-2)^2+(y-2)^2=1, then which of the following is true? a.maximum value of x+y is 4+sqrt(2) b.maximum value of x-y is sqrt(2) c.maximum value of x y is (9+4sqrt(2))/2 d.minimum value of x+y is 4-sqrt(2)

If y = f(x) and y^(4) - 4y + x = 0 . If f (-8) = 2 , then the value of |28 f' (- 8)| is

If x,y in R satisfy the equation x^2 + y^2 - 4x-2y + 5 = 0, then the value of the expression [(sqrtx-sqrty)^2+4sqrt(xy)]/((x+sqrt(xy)) is

If the circles x^(2) + y^(2) = k and x^(2) + y^(2) + 8x - 6y + 9 = 0 touch externally, then the value of k is