Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

At any point x , y on a curve if the length of the subnormal is x - 1 and the curve passes through 1 , 2 then the curve is a conic. A vertex of the curve is

Options

  1. A1 , 0
  2. B0 , 1
  3. C5 , 0
  4. D1 , 2

Correct answer

D. 1 , 2

Step-by-step solution

Let the curve be y = f x Length of subnormal is given by y d y d x i.e. y d y d x = x - 1 On integrating, we get y 2 2 = x 2 2 - x + C Given, the curve passes through 1 , 2 i.e. C = 5 2 So, y 2 = x 2 - 2 x + 5 or y 2 4 - x - 1 2 4 = 1 is an equation of a hyperbola. Its vertex would lie on 1 , ± 2

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 AP EAMCET PYQs