Is there any difference between the "general form" and "standard form" of a line?
I was thinking that there is no difference until I saw this exercise
1 Answer
$\begingroup$This might help you a bit;
There are 7 well known forms of Straight Lines:
General Form : $ax + by + c = 0$Significance: Any vector in the direction $ai + bj$ is perpendicular to this line.
Slope Intercept Form : $y = (\text{slope})x + (\text{$y$-intercept})$Significance: As the name suggests, one can write a line in this form to directly compare to get slope and the y-intercept.
One Point Slope form : $(y-y_1) = (\text{slope})(x-x_1)$ where $(x_1,y_1)$ is a point on the line
Two Point form : Just replace slope from above equation with $(\text{slope}) = (y_2-y_1)/(x_2 - x_1)$ where $(x_1,y_1) (x_2,y_2)$ are two points on the line.
Intercept form : $x/a + y/b = 1$ Significance: Here $a$ and $b$ represent algebraic length of $x$ and $y$ intercept of the line on the respective axis.
Normal Form: (This one is not much used for day to day purposes but its better to know something than not): Let length of normal from origin be $p$ making angle $\theta$ with the $x$-axis. Now put $p/\cos(\theta) = a$ and $p/\sin(\theta) = b$ in above intercept form.
Parametric Form: (Most powerful form of straight line) Put $x = h + r\cos(\theta)$ and $y =k + r \sin(\theta)$ where $r$ is a variable representing distance from a point $(h,k)$ on the line and $tan(\theta)$ is the slope of the line.
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