Slope Intercept Form, Two Point Form, Intercept Form, Circumcenter and Orthocenter Coordinates, Shifting of Origin, Distance between parallel lines with examples

This is the second video of Coordinate Geometry Chapter that I am currently teaching for you. In this video I have first explained to you the slope intercept form equation of a line to you. After that the two point form of the equation is explained and then the intercept form of the equation. By using all these three types the final equation which we are going to get will be the same because the basic concept behind all these three forms is the same. Then I have explained a slightly tough method of obtaining the coordinates of circumcenter of a triangle and then by a much similar method I have explained the method of obtaining the coordinates of the orthocenter of the triangle, After that I have explained the concept of shifting of origins and then the method of finding the perpendicular or shortest distance between two parallel lines. In most of these concepts wherever possible I have tried to prove the formula. Then while explaining I have explained some questions to make the concepts understandable to you. The questions discussed are listed below -

Ques 1. What will be the circumcenter of a triangle whose sides are (3x - y + 3 = 0), (3x + 4y + 3 = 0) and (x + 3y + 11 = 0)

Ques 2. The orthocenter of the triangle formed by the points (0,0), (8,0) and (4,6)

Ques 3. The points (p-1,p+2), (p,p+1) and (p+1,p) are collinear for which value of p ??

Ques 4. Find the equation of the straight line that passes through the points (1,2) and (7,8)

Ques 5. Find the equation of the straight line passing through (2,3) and parallel to the line 2x + 3y + 8 = 0

Ques 6. A point P whose coordinates are (3,-6), lies in the x-y plane. If the origin is shifted to the point (5,8), then what will be the coordinate of point P with respect to the new origin ??