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MaxWong

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MaxWong  13 janv. 2019
 #1
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Pick a pair of equations and solve the system of those equations, and you will get the vertices.

 

{y=x5x=2(x,y)=(2,7)

{y=x5y=15x+135(x,y)=(192,92)

{y=15x+135x=2(x,y)=(2,115)

 

We find the center of the circle by solving the system 

{(x2)2+(y+7)2=(x+192)2+(y92)2(x+192)2+(y92)2=(x2)2+(y115)2

which just says the squared distance from the center to each vertex is the same.

 

Solving gives the center coordinates (4910,125).

Radius of circle is just the distance between (4910,125) and any one of the vertices, i.e., (49102)2+(125115)2=231310.

We use center-radius form of circle equation, and we have the answer: (x+4910)2+(y+125)2=6877100

 

If you want a simpler answer, multiply both sides by 100 and get (10x+49)2+(10y+24)2=6877.

 

Exercise: Fill in the missed details in my solution.

3 mai 2022
 #1
avatar+9676 
+1
3 mai 2022