Lecture 1[03 Feb, 2020] MATH 127 (Prof Farid)

MATH -127 (Coordinate Geometry)
Chapter-1 (Change of Axes)

Change of Axes (Transformation of Coordinates)

        Changes of Axes:

(1) How to locate points on the coordinate or x-y plane:
    • Distance formula
    • Midpoint formula
    • Concept of line, circle, parabola etc

Some Equations to know:
        $$\begin{align*} & y = mx + c .......... \textrm{[slop intercept form]} \\ & y - y_1 = m (x - x_1) .......... \textrm{[point slop form]}\\ & P_n (x) = a_o + a_1 x + a_2 x^2 + \cdots + a_n x^n ~~~ where,~a_n \ne 0.......... \textrm{[Polynomial in x of degree n]}\\ & ~~~ if~~ n = 2,~~ p_2 (x) = y = a_o + a_1 x + a_2 x^2 .......... \textrm{[Equation of parabola]}\\ & ~~~ if~~ n = 1,~~ p_1(x) = y = a_o + a_1 x .......... \textrm{[Equation of line]} \end{align*}$$        

Transformation of coordinates:
    1. Translation
    2. Rotation

• General equation of second degree:   $ax^2 + 2hxy + b y^2 + 2 gx + 2 fy + c = 0$  

• Translation is the technique of removing the first degree

• Invariant: Same point different location.