santiagocelia832
Answered

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Determine the equation of the circle graphed below.
y
10
8
6
o
2
-10
-8
-6
4
-2
4
6
8
10
-2
-6
-10

Determine The Equation Of The Circle Graphed Below Y 10 8 6 O 2 10 8 6 4 2 4 6 8 10 2 6 10 class=

Sagot :

Nayefx

Answer:

(x-7)²+(y-4)²=3²

Step-by-step explanation:

to understand this

you need to know about:

  • circle equation
  • PEMDAS

tips and formulas:

  • circle equation standard form: (x-a)²+(y-b)²=r²

given:

  • (a,b)=(7,4)
  • r=3

let's solve:

  1. substitute the values of a,b and r :(x-7)²+(y-4)²=3³

and

we are done

View image Nayefx
MrRoyal

The equation of a circle is a measure of its center and its radius.

The equation of the circle is: [tex]x^2 + y^2 - 14x -8y + 56 = 0[/tex]

The general equation of a circle is [tex](x - a)^2 + (y - b)^2 + r^2[/tex]. Where:

[tex](a,b) \to[/tex] center

[tex]r \to[/tex] radius

From the given figure, we have:

[tex]r = 3[/tex]

[tex](a,b) = (7,4)[/tex]

So, the equation of the circle is:

[tex](x - a)^2 + (y - b)^2 + r^2[/tex]

[tex](x - 7)^2 + (y - 4)^2 = 3^2[/tex]

[tex](x - 7)^2 + (y - 4)^2 = 9[/tex]

Open brackets

[tex]x^2 - 14x + 49 + y^2 -8y + 16 = 9[/tex]

Collect like terms

[tex]x^2 + y^2 - 14x -8y + 49 + 16 - 9 = 0[/tex]

[tex]x^2 + y^2 - 14x -8y + 56 = 0[/tex]

Hence, the equation of the given circle is: [tex]x^2 + y^2 - 14x -8y + 56 = 0[/tex]

Read more about equations of circles at:

https://brainly.com/question/23988015

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