Question

Let F be the family of curves given by
x² + 2hxy + y² = 1, -1 < h < 1.
Then, the differential equation for the family of orthogonal trajectories to F is

• A. \((x^2y-y^3+y)\frac{dy}{dx}-(xy^2-x^3+x)=0\)
• B. \((x^2y-y^3+y)\frac{dy}{dx}+(xy^2-x^3+x)=0\)
• C. \((x^2y+y^3+y)\frac{dy}{dx}-(xy^2+x^3+x)=0\)
• D. \((x^2y+y^3+y)\frac{dy}{dx}+(xy^2+x^3+x)=0\)

Answer 1

The Correct Option is A

The correct option is (A) : \((x^2y-y^3+y)\frac{dy}{dx}-(xy^2-x^3+x)=0\).