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A circle has center (5. --4) and radius 8. Which gives the equation for the circle?
A. (x + 5)2 + (y + 4)2 = 8
B. (X - 5)2 + y + 4)2 = 8
C. (x + 5)2 + (y – 412
D. (x - 5)2 + (y + 4)2

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Answer:

(x-5)^2 + (y+4)^2 =64

Step-by-step explanation:

We can write the equation of a circle as

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-5)^2 + (y- -4)^2 = 8^2

(x-5)^2 + (y+4)^2 =64

Lanuel

the equation for the circle is given by the mathematical expression: [tex](x - 5)^2 + (y + 4)^2 = 8^2[/tex]

Given the following data;

  • h = 5
  • k = -4
  • Radius, r = 8

In Mathematics, the general equation for a circle is given by the formula;

[tex]x^2 + y^2 + 2hx + 2ky + c = 0[/tex]  ......equation 1.

Where the center is C(-h, -k)

Also, the standard form of the equation of a circle is;

[tex](x - h)^2 + (y - k)^2 = r^2[/tex] ......equation 2.

Where;

  • h and k represents the coordinates of the center.
  • r represents the radius of the circle.

Substituting the values into equation 2, we have;

[tex](x - 5)^2 + (y - [-4])^2 = 8^2\\\\(x - 5)^2 + (y + 4)^2 = 8^2[/tex]

Simplifying further, we have;

[tex](x - 5)^2 + (y + 4)^2 = 64[/tex]

Therefore, the equation for the circle is given by the mathematical expression: [tex](x - 5)^2 + (y + 4)^2 = 8^2[/tex]

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