Tuesday, February 26, 2019
Straight line equations (first degree)
- Ax +By +C = 0( General form)
- x=0. (Y-axis)
- y =0 (x-axis)
- x = a (Parallel to y-axis)
- y = b (Parallel to x axis)
- The distance of a point (x ,y) from x-axis is |y| and from y-axis |x|.
- Y=mx +c. Line which cuts off an intercept c on y-axis and makes an angle θ with the positive direction (anticlockwise) of x-axis and tanθ = m is called its slope or gradient.
- y = m x. Any line through the origin.
- (x/a)+(y/b) = 1. Intercept form: Here a and b are the intercepts on the axis of the x and y respectively.
- In this case the position AB of the line intercepts between the axes is the length √(a2 +b2 ) by Pythagoras rule.
- y-y1 = m(x-x1 ). Equation of straight line through a given point (x1 , y1 ) and having slope m i.e. tanθ=m.
- Note: (y-y1 )/(x-x1 )=m. If m=0 i.e. the line is parallel to to x- axis, then its equation will be Nr = 0 or y-y1 =0. If m = ∞i.e. the line is perpendicular to x-axis, then its equation will be Dr=0 or x-x1 =0.
- Y-y1 =[(y2 -y1 )/(x2 -x1 )](x-x1 )Equation of a straight line passing through two given points(x1 , y1 ) and (x2 , y2 ).
- Xcos α +ysin α = p. equation of a line on which the length of perpendicular from origin is p and α is the angle which this perpendicular makes with the positive direction of x-axis.
- Parametric form of a straight line: (x-x1 )/cosθ=(y-y1 )/sinθ=r this is another form