Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2016MathematicsDifferential Equations

The differential equation of the family of circles touching y-axis at the origin is

Options

  1. Ax 2 + y 2 d y d x - 2 x y = 0
  2. Bx 2 - y 2 + 2 x y d y d x = 0
  3. Cx 2 - y 2 d y d x - 2 x y = 0
  4. Dx 2 + y 2 d y d x + 2 x y = 0

Correct answer

B. x 2 - y 2 + 2 x y d y d x = 0

Step-by-step solution

As required circle touches y - axis at the origin. ∴ Let Center of the circle is d ( a , 0 ) and radius is a ∴ Equation of circle will be, x - a 2 + y - 0 2 = a 2 ⇒ x 2 - 2 a x + a 2 + y 2 = a 2 ⇒ x 2 + y 2 - 2 a x = 0 .... (i) By differentiating above equation w.r.t x, we get 2 x + 2 y d y d x - 2 a = 0 ∴ 2 a = 2 x + 2 y d y d x .... (ii) From (i) and (ii), x 2 + y 2 - 2 x + 2 y d y d x x = 0 ⇒ x 2 + y 2 - 2 x 2 - 2 x y d y d x = 0 ⇒ x 2 - y 2 + 2 x y d y d x = 0

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