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 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 equation of all conics whose centre k 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

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

Form the differential equation of y=px+(p)/(sqrt(1+p^(2).

The differential equation satisfying the curve (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 when lambda begin arbitary uknowm, 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

If p is the length of the perpendicular from the origin to the line (x)/(a) + (y)/(b) = 1, "then prove that " (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2))

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that locus of the O centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2)) .

The lines given by the equation (2y^2+3xy-2x^2)(x+y-1)=0 form a triangle which is