What does the equation `xdy=ydx` represent?

Options

A. A family of circles
B. A family of parabolas
C. A family of hyperbolas
D. A family of straight lines

Answer

D

Explanation

Given equation is x dy = y dx
By separating the variable we get
`(dy)/y = (dx)/x`
On integrating both sides, we get
` int (dy)/y = int (dx)/x`
` Rightarrow log y= log x + log c`
` Rightarrow y =cx`
It represents a family of straight lines.