Answer to Question #183884 in Analytic Geometry for Nina

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

"(x-a)^2 + (y-b)^2 =r^2"

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

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

Eliminating "r^2"

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

"(81-18a+a^2 + 1089-66b+b^2)-(729-54a+a^2+225+30b+b^2)=0""81+1089-729-225-18a+54a-66b-30b +a^2-a^2+b^2-b^2=0""216+36a-96b=0"

dividing through by 12 yields

"3a-8b+18=0"

Axle equation:

"3y+2x-7=0."

it passes at "(a,b)"

hence

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

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

"6a+9b-21=0"

"-"

"6a-16b+36=0"

"25b-57=0"

"b=57\/25"

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

"2a-4\/25=0"

"2a=4\/25"

"a=2\/25"

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

Equation of the wheel becomes"(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)" ,center is "C(2\/25, 57\/25)"

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

"r^2= ((9-2\/25)^2+(33-57\/25)^2)=1023.2848"

"r=32 units"

hence equation of the circle becomes

"(x-2\/25)^2+(y-57\/25)^2=32^2"

Sketching this gives:


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