Answer to Question #180995 in Geometry for dazai

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

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

therefore,

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

$x^2-18x+ 81+y^2 - 66y + 1089 = x^2 - 54x + 729 + y^2 + 30y+225$

it can be simplified to

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

Equation of the axle is given by;

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

Solving the two equations simultaneously

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

thus y= 57/25

replace y in (eqn2)

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

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

Graph illustrating of the solution is attached.