Question #180995

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.


1
Expert's answer
2021-05-11T13:00:57-0400

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

therefore,

(x9)2+(y33)2=(x27)2+(y(15))2(x - 9)^2 + (y - 33)^2 = (x - 27)^2 + (y - (-15))^2


x218x+81+y266y+1089=x254x+729+y2+30y+225x^2-18x+ 81+y^2 - 66y + 1089 = x^2 - 54x + 729 + y^2 + 30y+225


it can be simplified to

36x96y=2166x16y=26.............(eqn1)36x - 96y= - 216 \newline 6x - 16y = -26 ............. (eqn1)


Equation of the axle is given by;

3y+2x=7...........(eqn2)3y + 2x = 7........... (eqn2)

Solving the two equations simultaneously


(2x+3y=7)36x16y=26(2x +3y = 7)*3\newline 6x - 16y = -26


thus y= 57/25

replace y in (eqn2)


2x+3(57/25)=7x=2/252x + 3( 57/25) = 7\newline x = 2/ 25


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

Graph illustrating of the solution is attached.



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