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Math  /  Geometry

QuestionWrite the standard form of the equation of the circle with the given center and radius. Center (−4,−5),r=2(-4,-5), r=\sqrt{2}
The equation of the circle in standard form is □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. The center of the circle is given as (−4,−5)(-4, -5).
2. The radius of the circle is given as r=2r = \sqrt{2}.

STEP 2

1. Recall the standard form equation of a circle.
2. Substitute the center and radius into the equation.
3. Simplify the equation.

STEP 3

Recall the standard form equation of a circle:
(x−h)2+(y−k)2=r2 (x - h)^2 + (y - k)^2 = r^2
where (h,k)(h, k) is the center of the circle and rr is the radius.

STEP 4

Substitute the given center (−4,−5)(-4, -5) and radius r=2r = \sqrt{2} into the equation:
(x−(−4))2+(y−(−5))2=(2)2 (x - (-4))^2 + (y - (-5))^2 = (\sqrt{2})^2

STEP 5

Simplify the equation:
(x+4)2+(y+5)2=2 (x + 4)^2 + (y + 5)^2 = 2
The equation of the circle in standard form is:
(x+4)2+(y+5)2=2 \boxed{(x + 4)^2 + (y + 5)^2 = 2}

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