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 straight lines which are at a fixed distance of 10 units from the origin is (y-xy_(1))^(2) = A(1+y_(1)^(2)) then A is equal to ________.

The differential equation of all conics whose centre klies 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

If y=(log)_e(x/a)^x ,then x^3y_2= (a) (xy_1-y)^2 (b) ((y-x y_1)/(y_1))^2 (c) none of these

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

Equation of pair of straight lines drawn through (1, 1) and perpendicular to the pair of lines 3x^(2)-7xy+2y^(2)=0 , is

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

The solution of differential equation y'(1+x^(2))=2xy is :

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these

Prove that the line passing through the points (x_(1),y_(1)) and (x_(2),y_(2)) is at a distance of |(x_(1)y_(2)-x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))| from origin.

The distance from the foci of P (x_(1), y_(1)) on the ellipse x^2/9+y^2/25=1 are