Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20239 May 2023Evening ShiftMathematicsDifferential EquationsActual

The differential equation of all circles which pass through the origin and whose centres lie on Y -axis is

Options

  1. A(x^2-y^2 ) d y d x -2 x y=0
  2. B(x^2-y^2 ) d y d x +2 x y=0
  3. C(x^2-y^2 ) d y d x +x y=0
  4. D(x^2-y^2 ) d y d x -x y=0

Correct answer

A. (x^2-y^2 ) d y d x -2 x y=0

Step-by-step solution

Circle passes through origin and centre lie on Y -axis. Let (0, k) be centre and ' k ' be radius Equation of circle is aligned & (x-0)^2+(y- k )^2= k ^2 & x^2+y^2-2 y k + k ^2= k ^2 & x^2+y^2-2 k y=0 & x^2+y^2=2 k y ...(i) & x^2+y^2 2 y = k ...(ii) aligned Differentiating equation (i) with respect to x , we get aligned & 2 x+2 y d y ~d x =2 k d y ~d x & 2 x+2 y d y ~d x -2 k d y ~d x =0 & 2 x+2(y- k ) d y ~d x =0 & 2 x+2 [y- ( x^2+y^2 2 y ) ] d y ~d x =0 ...[From(ii)] & 2 x+2 [ 2 y^2-x^2-y^2 2 y ] d y ~d x =0 & 2 x

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is 2025The general solution of the differential equation (x+y) d y=d x is 2025If Ax ^3+ Bxy =4 (A and B are arbitrary constants) is the general solution of the differential equation F(x) d^2 y d x^2 +G(x) d y d x -2 y=0 , then F(1)+G(1)= 2025If y=A t^2+ B t (A,B are parameters) is general solution of the differential equation f(t) y^ (t)+g(t) y^ (t)+h(t) y=0 then 2 f(t)+t^2 h(t)= 2025The general solution of the differential equation (2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0 is 2025The general solution of the differential equation x x d y=(x x-y) d x is 2025If a and b are arbitrary constants, then the differential equation corresponding to the family of curves y= (a x+b) is 2025The general solution of the differential equation x y(y+2) d y+ (y^3-1 ) d x=0 is 2025 Full Differential Equations list All MHT CET PYQs