Question #183884

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
2021-05-04T13:17:03-0400

(xa)2+(yb)2=r2(x-a)^2 + (y-b)^2 =r^2

(9a)2+(33b)2=r2(9-a)^2 + (33-b)^2 =r^2

(27a)2+(15b)2=r2(27-a)^2 + (-15-b)^2 =r^2

Eliminating r2r^2

((9a)2+(33b)2)((27a)2+(15b)2)=0((9-a)^2 + (33-b)^2) -((27-a)^2 + (-15-b)^2)=0

(8118a+a2+108966b+b2)(72954a+a2+225+30b+b2)=0(81-18a+a^2 + 1089-66b+b^2)-(729-54a+a^2+225+30b+b^2)=081+108972922518a+54a66b30b+a2a2+b2b2=081+1089-729-225-18a+54a-66b-30b +a^2-a^2+b^2-b^2=0216+36a96b=0216+36a-96b=0

dividing through by 12 yields

3a8b+18=03a-8b+18=0

Axle equation:

3y+2x7=0.3y+2x-7=0.

it passes at (a,b)(a,b)

hence

(3a8b+18=0).2(3a-8b+18=0).2

(2a+3b7=0).3(2a+3b-7=0).3

6a+9b21=06a+9b-21=0

-

6a16b+36=06a-16b+36=0

25b57=025b-57=0

b=57/25b=57/25

2a+3(57/25)7=02a+3*(57/25)-7=0

2a4/25=02a-4/25=0

2a=4/252a=4/25

a=2/25a=2/25

Thus the center of the wheel is at (2/25,57/25)(2/25, 57/25)

Equation of the wheel becomes(x2/25)2+(y57/25)2=r2(x-2/25)^2+(y-57/25)^2=r^2

now we must get radius r

one point on the circumference is A(9,33)A(9,33) ,center is C(2/25,57/25)C(2/25, 57/25)

thus the radius is the magnitude of the distance between A and C

r2=((92/25)2+(3357/25)2)=1023.2848r^2= ((9-2/25)^2+(33-57/25)^2)=1023.2848

r=32unitsr=32 units

hence equation of the circle becomes

(x2/25)2+(y57/25)2=322(x-2/25)^2+(y-57/25)^2=32^2

Sketching this gives:


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