If `x^(2)+4y^(2)-8x+12=0` is satisfied by real values of `x` and `y` then `x` lies between

If x^2 + 4y ^2 - 8x +12 =0 is satified by real values of x nad y then y must lies between

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

If the area of the circle 4x^(2)+4y^(2)-8x+16y+k=0 is 9pi square units, then the value of k 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 a point (a, sqrt(a)) lies in region bounded between the circles x^(2) + y^(2) + 4x + 4y + 7 = 0 and x^(2) + y^(2) + 4x + 4y -1 = 0 , then the number of integral values of a exceeds

If x is real, then the value of the expression (x^2+14 x+9)/(x^2+2x+3) lies between

The circumference of the circle x^2+y^2-2x+8y-q=0 is bisected by the circle x^2+ y^2+4x+12y+p=0 , then p+q is equal to

(i) Find the length of the chord intercepted by the circle x^(2)+y^(2)-8x-2y-8=0 on the line x+y+1=0 (ii) Find the length of the chord intercepted by the circle x^(2)+y^(2)+8x-4y-16=0 on the line 3x-y+4=0 (iii) Find the length of the chord formed by x^(2)+y^(2)=a^(2) on the line xcos alpha +y sin alpha=p