Answer to Question #209445 in Analytic Geometry for liv

Question

B ​​Quadratics in Motion: (​7, 6)

C​ Towers of Trigonometry: (​2, 14) D​​ The Food Equation: (​5, 8) 

Every square on the graph equals 60 m in the park. Jane and Bob are going to design a circular Ride that goes through the points B, C and D. 

1. Help them calculate where the centre of the ride would be.

Answer 1

The equaiton of the circle is

$(x-a)^2+(y-b)^2=R^2$

$(7-a)^2+(6-b)^2=R^2$

$(2-a)^2+(14-b)^2=R^2$

$(5-a)^2+(8-b)^2=R^2$

$49-14a+a^2+36-12b+b^2$

$=4-4a+a^2+196-28b+b^2$

$25-10a+a^2+64-16b+b^2$

$=4-4a+a^2+196-28b+b^2$

$10a-16b=-115$

$6a-12b=-111$

$30a-60b-30a+48b=-555+345$

$6a-12b=-111$

$12b=210$

$6a=210-111$

$a=16.5$

$b=17.5$

Center $(16.5, 7,5).$