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 $(16.5, 7,5).$