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.
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