Question

Solve this question!​

Answer 1

Step-by-step explanation:

Differentiating the above equation we have

$2x + 2 y\frac{dy}{dx} = 0$

$\frac{dy}{dx} = \frac{ - x}{y}$

Now for orthogonal trajectories, the slope at point will be

$\frac{dy}{dx} = \frac{ - 1}{ \frac{ - x}{y} } = \frac{y}{x}$

Separating the variables and integrating the equation we have,

$\frac{dy}{y} = \frac{dx}{x}$

$ln(y) = ln(x) + ln(c)$

$y = kx$

Where k is a constant