The differential equation of all straight lines which are at a constant distance p from the origin, is
(a) `(y+xy_1)^(2)=p^(2) (1+y_(1)^2)`
(b) `(y-xy_(1)^(2))=p^(2) (1+y_(1))^(2)`
( c ) `(y-xy_(1))^(2)=p^(2) (1+y_(1)^(2))`
(d) None of these

The differential equation of all circle of radius r, is given by (a) {1+(y_(1))^(2)}^(2)=r^(2)y_(2)^(3) (b) {1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(3) ( c ) {1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(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 satisfying the curve (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 where lambda be arbitary uknown, is (a) (x+yy_(1))(xy_(1)-y)=(a^(2)-b^(2))y_(1) (b) (x+yy_(1))(xy_(1)-y)=y_(1) ( c ) (x-yy_(1))(xy_(1)+y)(a^(2)-b^(2))y_(1) (d) None of these

The distance of the point (1, 2, 1) from the line (x-1)/(2) = (y-2)/(1)=(z-3)/(2) is

The distance of the point (1,2,1) from the line (x-1)/2=(y-2)/1=(z-3)/2 is

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

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

For the differential equation xy(dy)/(dx)=(x+2)(y+2) , find the solution curve passing through the point (1, -1).

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