Question

can someone explain me parametric form of a line? My textbook just says parametric form of line is \[\frac{x-x_1}{cos\theta}=\frac{y-y_1}{sin\theta}=r\] and i don't understand it.

Answer 1

\(\theta\) is inclination of line.

Answer 2

since in a right angled triangle we have polar co-ordinates as
\[\tan \theta=gradient=\Delta y/\Delta x\]
\[\sin \theta/\cos \theta=\Delta y/\Delta x\]
cross-multiply
\[\Delta x/\cos \theta =\Delta y/\sin \theta\]
both these are equal to r since
\[\cos \theta=x/r,\sin \theta=y/r\]
\[r=\Delta x/\cos \theta=\Delta y/\sin \theta\]

Answer 3

So, \(\Delta x\)=\(x-x_1\) for any arbitrary value of x where \(x_1\) is constant. right?

Answer 4

yes that is correct...

Answer 5

thanks mate!

Answer 6

sure thing