The differential equation of all circle in the first quadrant touch the coordinate is
(a) `(x-y)^(2)(1+y')^(2)=(x+yy')^(2)`
(b) `(x-y)^(2)(1+y')^(2)=(x+y')^(2)`
( c ) `(x-y)^(2)(1+y')=(x+yy')^(2)`
(d) None of these

The differential equations of all circle touching the x-axis at orgin is (a) (y^(2)-x^(2))=2xy((dy)/(dx)) (b) (x^(2)-y^(2))(dy)/(dx)=2xy ( c ) (x^(2)-y^(2))=2xy((dy)/(dx)) (d) None of these

The differential equation of all conics whose centre lies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

y = sqrt(1 + x^(2)) : y' = (xy)/(1 + x^(2))

If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y_(2) + 2x (x^(2) + 1)y_(1) = 2

Obtain equation of circle in x^(2) + y^(2) - x + y = 0

Area lying in the first quadrant and bounded by the circle x^(2) + y^(2) = 4 and the lines x = 0 and x = 2 is

Area lying in the first quadrant and bounded by the circle x^2 +y^2 =4 and the line x=0 and x=2 is