The range of values of `alpha` for which the line `2y=gx+alpha` is a normal to the circle `x^2=y^2+2gx+2gy-2=0` for all values of `g` is (a)`[1,oo)` (b) `[-1,oo)` (c)`(0,1)` (d) `(-oo,1]`

The line ax+by+by+c=0 is normal to the circle x^(2)+y^(2)+2gx+2fy+d=0, if

The equation of the normal at P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 is

If alpha is the angle subtended at P(x_(1),y_(1)) by the circle S-=x^(2)+y^(2)+2gx+2fy+c=0 then

If alpha is the angle subtended at P(x_(1),y_(1)) by the circle S-=x^(2)+y^(2)+2gx+2fy+c=0 then

If alpha is the angle subtended at P(x_(1),y_(1)) by the circle S-=x^(2)+y^(2)+2gx+2fy+c=0 then

The line y=m x-((a^2-b^2)m)/(sqrt(a^2+b^2m^2)) is normal to the ellise (x^2)/(a^2)+(y^2)/(b^2)=1 for all values of m belonging to (0,1) (b) (0,oo) (c) R (d) none of these

The line y=m x-((a^2-b^2)m)/(sqrt(a^2+b^2m^2)) is normal to the ellise (x^2)/(a^2)+(y^2)/(b^2)=1 for all values of m belonging to (a) (0,1) (b) (0,oo) (c) R (d) none of these

Find the set of values of a for which the equation |x-1|^2+(a-1)|x-1|+1=0 has a solution, [2,5] b. [-3,-1] c. [0,oo) d. (-oo,-1]

The range of parameter ' a ' for which the variable line y=2x+a lies between the circles x^2+y^2-2x-2y+1=0 and x^2+y^2-16 x-2y+61=0 without intersecting or touching either circle is (a) a in (2sqrt(5)-15 ,0) (b) a in (-oo, 2sqrt(5)-15,) (c) a in (2sqrt(5)-15,-sqrt(5)-1) (d) a in (-sqrt(5)-1,oo)