Which equation represents a circle whose center is located at ( - 6, 2) and whose radius is sqrt (10) units?

The equation of the given circle is (x+6) ² + (y-2) ² = 10 or x² + y² + 12x - 4y + 30 = 0

Step-by-step explanation:

Step 1:

Center of the given circle = (-6,2)

Radius = √10 units

We need to find the equation of this circle.

Step 2:

Circle's equation with center at (h, k) and radius of r units is given by

(x-h) ² + (y-k) ² = r²

So substituting the above values

we have

(x - (-6)) ² + (y-2) ² = (√10) ²

(x+6) ² + (y-2) ² = 10

Simplifying, this can be written as

x² + 36 + 12x + y² + 4 - 4y = 10

x² + y² + 12x - 4y + 30 = 0

Step 3:

Answer:

The equation of the given circle is (x+6) ² + (y-2) ² = 10 or x² + y² + 12x - 4y + 30 = 0