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 differintial eauation 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 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 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

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/(p^2)

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

Three points P(h,k), Q(x_(1) , y_(1) ) and R(x_(2) , y_(2) ) lie on a line. Show that, (h-x_(1) ) (y_(2) -y_(1) ) = (k-y_(1) ) ( x_(2) - x_(1) ) .