Identify the curve `sqrt((x+1)^(2)+y^(2))+ sqrt(x^(2)+(y-1)^(2))-2`=0

The portion of the tangent to the curve x=sqrt(a^(2)-y^(2))+(a)/(2)(log(a-sqrt(a^(2)-y^(2))))/(a+sqrt(a^(2)-y^(2))) intercepted between the curve and x -axis,is of legth.

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

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)

if,sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then prove that x sqrt(1-x^(2))+y sqrt(1-y^(2))+z sqrt(1-z^(2))=2xyz

An equation of the curve satisfying x dy - y dx = sqrt(x^(2)-y^(2))dx and y(1) = 0 is

Let y= y(x) be a solution the diFIGUREFIGUREerential equation, sqrt ( 1- x^(2) ) (dy)/(dx) + sqrt (1-y^(2) )=0 ,|x|lt 1. IFIGURE y((1)/(2))= (sqrt (3) )/(2), then y((-1)/(sqrt(2))) is equal to:

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)

" 24.Show that the equation of tangent at the point "P(x_(1)+y_(1))" on the curve "sqrt(x)+sqrt(y)=sqrt(a)" is "xx_(1)^((-1)/(2))+yy_(1)^((-1)/(2))=a^((1)/(2))

The solution of x sqrt(1+y^(2))dx+y sqrt(1+x^(2))dy=0