Let be a line through cutting the line and forming an angle . Prove that the equation of the line is
or
Hello GTK X HunterI think you have an error in the second of these two equations. Here is what I believe to be the correct result.
The equation of the line with gradient passing through the point isThis makes an angle , say, with the direction of the -axis, where .
The line makes an angle , say, with the -axis, where .
Then, depending on which side of the line the angle is made:(See the attached diagram. The lines shown are not necessarily the actual lines, but simply parallel to them through a single point.)So the two gradients are and .
The error in the question can be easily verified, because the gradient of one of the the given lines is the gradient of the other. Therefore they make equal angles above and below the -axis. They should, of course, make equal angles above and below the line .
Grandad