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What is the general form of the equation for the given circle?

A. x2 + y2 − 8x − 8y + 23 = 0

B. x2 + y2 − 8x − 8y + 32 = 0

C. x2 + y2 − 4x − 4y + 23 = 0

D. x2 + y2 + 4x + 4y + 9 = 0

What is the general form of the equation for the given circle A x2 y2 8x 8y 23 0 B x2 y2 8x 8y 32 0 C x2 y2 4x 4y 23 0 D x2 y2 4x 4y 9 0 class=

Respuesta :

frika

Answer:

A [tex]x^2+y^2-8x-8y+23=0[/tex]

Step-by-step explanation:

From the diagram you can see that the center of the circle is placed at point O(4,4). The radius of the circle is

[tex]r=AO=\sqrt{(4-4)^2+(7-4)^2}=\sqrt{0^2+3^2}=\sqrt{9}=3.[/tex]

Thus, the equation of the circle is

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

Rewrite it

[tex]x^2-8x+16+y^2-8y+16=9,\\ \\x^2+y^2-8x-8y+32-9=0,\\ \\x^2+y^2-8x-8y+23=0.[/tex]

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