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Math  /  Geometry

QuestionGraph the circle which is centered at (−7,−6)(-7,-6) and has a radius of 2 units.

Studdy Solution

STEP 1

1. The center of the circle is at the point (−7,−6)(-7, -6).
2. The radius of the circle is 22 units.

STEP 2

1. Recall the standard equation of a circle.
2. Substitute the center and radius into the equation.
3. Simplify and write the equation of the circle.
4. Plot the center and use the radius to draw the circle.

STEP 3

Recall the standard 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 center (−7,−6)(-7, -6) and radius 22 into the equation:
(x+7)2+(y+6)2=22 (x + 7)^2 + (y + 6)^2 = 2^2

STEP 5

Simplify the equation:
(x+7)2+(y+6)2=4 (x + 7)^2 + (y + 6)^2 = 4

STEP 6

To graph the circle: - Plot the center of the circle at (−7,−6)(-7, -6). - From the center, measure a distance of 22 units in all directions (up, down, left, right) to mark points on the circle. - Draw a smooth curve connecting these points to form the circle.
The equation of the circle is:
(x+7)2+(y+6)2=4 \boxed{(x + 7)^2 + (y + 6)^2 = 4}

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