Answer to Question #182225 in Geometry for l65656kk

Question

Ferris wheel cars are at a position of A (9,33) and B (27,-15). One of its axle is

represented by 3y+2x-7= 0 where it passes through the center of the wheel.

Draw the suitable graph of the said situation.

Answer 1

Solution

Let the center of the Ferris wheel to be (x, y)

therefore,

(x - 9)² + (y - 33)² = (x - 27)² + (y - (-15))²

x²-18x+ 81+y² - 66y + 1089 = x² - 54x + 729 + y² + 30y+225

it can be simplified to

36x - 96y= - 216 or

6x - 16y = -26 (eqn1)

Equation of the axle is given by;

3y + 2x = 7 (eqn2)

Solving the two equations simultaneously

(2x +3y = 7)*3

6x - 16y = -26

thus y= 57/25

replace y in (eqn2)

2x + 3( 57/25) = 7

x = 2/ 25

Thus the center of the Ferris wheel is given by ( 2/ 25, 57/25 )

Below is a graph illustrating the solution: