Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2023MathematicsDifferential EquationsActual

A parabola pases through (1,2) and satisfies the differential equation d y d x = 2 y x , x 0, y 0 . What is the directrix of the parabola?

Options

  1. Ay=- 1 8
  2. By= 1 8
  3. Cx=- 1 8
  4. Dx= 1 8

Correct answer

A. y=- 1 8

Step-by-step solution

aligned & Since, d y d x = 2 y x & d y y = 2 d x x y=2 x+ c y=x^2 c & it satisfy (1,2) & 2=1 C C=2 y=2 x^2 aligned Since, y=2 x^2 x^2= 1 2 y x^2=4 1 8 y So, directrix of Parabola is y=- 1 8

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is d^2y dx^2 ( dx dy )^2 equal to ? 2026What is the solution of the differential equation ( dy dx )=p when y(0)=q ? 2026Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is the solution of the differential equation with y(0)=0 ? 2026What is the degree of the differential equation ( d^2y dx^2 )^ 3 2 = ( dy dx )^ 5 2 ? 2025If k is an arbitrary constant, then what is the general solution of the equation (x + y)^2 dy dx = k^2 ? 2025Consider the following statements: I. y = xe^ 2x is the solution of dy dx = y (2 + 1 x ) . II. y = x |x| + cx is the solution of dy dx = x + y x . Which of the statements given abo 2025What are the order and degree respectively of the differential equation 2- ( d y d x )^2 ^ 0.6 = d^2 y d x^2 ? 2024Paragraph: Let y d x+ (x-y^3 ) d y=0 be a differential equation. Question: What is the solution of the differential equation? 2024 Full Differential Equations list All NDA PYQs