Question

1.)

The center of a circle (h, k) is (6,2)
The radius (r) is 8
What is the correct equation of the circle in Standard Form.
(x - h)² + (y - k)² = r²

A.) (x+6)² + (y+2)² = 8²
B.) (x-6)² + (y-2)² = 8²
C.) (x-6)² + (y+2)² = 8²
D.) (x+6)² + (y-2)² = 8²

2.)
What is the center and radius of the circle given in the following equation in General Form?

x² + y² - 4x + 2y - 4 = 0

A.) Center (-2,-1) radius = 3
B.) Center (2,1) radius = 9
C.) Center (4,7) radius = 8
D.) Center (2,-1) radius = 3

Answer 1

Answer:

1. C.) (x-6)² + (y+2)² = 8².

2. D.) Center (2,-1) radius = 3.

Explanation:

1.) Using the given information, we have:

Center of the circle (h, k) = (6, 2)
Radius (r) = 8

Using the standard form of the equation of a circle, we get:

(x - h)² + (y - k)² = r²

Substituting the values we get:

(x - 6)² + (y - 2)² = 8²

So, the correct equation of the circle in standard form is option C.) (x-6)² + (y+2)² = 8².

2.) To find the center and radius of the circle given in general form, we need to convert it into standard form. Completing the square, we get:

(x² - 4x + 4) + (y² + 2y + 1) = 4 + 1 + 4

(x - 2)² + (y + 1)² = 3²

So, the center of the circle is (2, -1) and the radius is 3. Therefore, the correct answer is option D.) Center (2,-1) radius = 3.