Use triginometry to solve this problem A car moves from poin

Use triginometry to solve this problem. A car moves from point A to point B. Radius R = 150 point A is (400, 200), point B is (1500, 400), point R is (600, 100) Question is to find the coordinates at point M? What are the components of x and y at pt M?

Solution

coordinates of A = ( 400,200)

B = ( 1500,400)

from this we will find the equation of the line AB

slope = 400- 200/1500 - 400 = 2/11

hence, equation of line AB : y = 2/11x + 1400/11

now we have coordiantes of radius which is centre ( 600,100)

and radius length = 150

hence we can find the equation of the circle from this

( x- 600)^2 + ( y - 100)^2 = 150^2

the point of intersection of circle and line will give the coordinates of M:

substitute y =2/11x + 1400/11

(x -600)^2 + (2/11x + 1400/11 - 100)^2 = 150^2

on solving the quadratic we get two values : x = 510 , 642

y = (2/11)*510 + 1400/11 = 220

y = (2/11)*642 + 1400/11 =244

Solution : Coordinates of (x , y) = ( 642 , 244)