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=(log)_(e)((x)/(a))^(x), thenx ^(3)y_(2)=b)(xy_(1)-y)^(2).(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

The degree of the differential equation satisfying the relation sqrt(1+x^(2))+sqrt(1+y^(2))=lambda(x sqrt(1+y^(2))-y sqrt(1+x^(2)))

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

Find the degree of the differential equation satisfying the relation sqrt(1+x^(2))+sqrt(1+y^(2))=lambda(x sqrt(1+y^(2))-y sqrt(1+x^(2)))

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=sin(m sin^(-1)x), then (1-x^(2))y_(2)-xy_(1) is equal to m^(2)y(b)my(c)-m^(2)y(d) none of these

Form differential equation for (x-a)^(2)+y^(2)=a^(2) A) (x+yy_(1))^(2)=y^(2) B) (xy_(1)+y)^(2)=y^(2) C) y^(2)=x^(2)+2xyy_(1) D) x^(2)=y^(2)+2xyy_(1)

Show that the equation of the tangent to the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 " at " (x_(1), y_(1)) " is " ("xx"_(1))/(a^(2)) - (yy_(1))/(b^(2)) = 1

Show that the equation of the tangent to the ellipse (x^(2))/(a^(2))+ (y^(2))/(b^(2)) = 1 " at " (x_(1), y_(1)) " is " ("xx"_(1))/(a^(2)) + ("yy"_(1))/(b^(2)) = 1