" (b) "x^(2)-y^(2)=a^(2)" and "x^(2)+y^(2)=a^(2)sqrt(2)

if a>2b>0, then positive value of m for which y=mx-b sqrt(1+m^(2)) is a common tangent to x^(2)+y^(2)=b^(2) and (x-a)^(2)+y^(2)=b^(2) is

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)-y^(2))) div (sqrt(x^(2)-y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

If x ^(2)y^(2) =tan ^(-1) sqrt(x^(2) +y^(2) )+cot ^(-1) sqrt(x^(2) +y^(2)),then (dy)/(dx)=

The equation of a circle of radius 1touching the circles x^(2)+y^(2)-2|x|=0 is x^(2)+y^(2)+2sqrt(2)x+1=0x^(2)+y^(2)-2sqrt(3)y+2=0x^(2)+y^(2)+2sqrt(3)y+2=0x^(2)+y^(2)-2sqrt(2)+1=0

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)-y^(2)))-:(sqrt(x^(2)-y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

Equation of a line which is tangent to both the curve y=x^(2)+1 and y=x^(2) is y=sqrt(2)x+(1)/(2) (b) y=sqrt(2)x-(1)/(2)y=-sqrt(2)x+(1)/(2)(d)y=-sqrt(2)x-(1)/(2)

Find y ' , if (a) y=5x^(2//3)-3x^(5//2)+2x^(-3) (b) y=(a)/(3sqrt(x))^(2)-(b)/(x^(3)sqrt(x) (a,b constants )

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)+y^(2)))-:(sqrt(x^(2)+y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

If (sqrt(a + 2b) + sqrt(a - 2b))/(sqrt(a + 2b) - sqrt(a - 2b)) = sqrt3 and a^(2) + b^(2) = 1 , then the find values of a and b. (b) If sqrt((x - sqrt(a^(2) - b^(2)))^(2) + y^(2)) + sqrt((x + sqrt(a^(2) - b^(2)))^(2) + y^(2)) = 2a then prove that (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1