Respuesta :

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Answer:

(x+3)² + (y+4)²=25

Step-by-step explanation:

The question is on equation of a circle

The distance formula is given by;

√(x-h)²+ (y-k)²=r

The standard equation of  circle is given as ;

(x-h)²+ (y-k)²=r²

The equation of this circle with center (-3, -4) and radius 5 will be;

(x--3)² + (y--4)²=5²

(x+3)² + (y+4)²=25

kudzordzifrancis

ANSWER

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

EXPLANATION

The equation of a circle with center (h,k) and radius r units is given by:

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

From the given information the center of the circle is (-3,-4) and the radius is r=5 units.

We substitute the known values to obtain:

[tex]{(x - - 3)}^{2} + {(y - - 4)}^{2} = {5}^{2} [/tex]

We simplify to get:

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

Therefore the equation of the circle in standard form is:

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

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