Question

50 points!! help asap pls

Write the equation of a circle with a radius of length 10 and a center at (-4, -9).

Answer choices in attached image

Answer 1

Option D

Explanation:

Given:

• Radius = 10 units
• Center point = (h, k) = (-4, -9)

∴ x coordinate of center point: (h, k) ⇒ (-4, -9)

∴ y coordinate of center point: (h, k) ⇒ (-4, -9)

Equation of circle formula:

• ⇒ (x - h)² + (y - k)² = r²

Substitute the radius in the formula;

• ⇒ (x - h)² + (y - k)² = r²

• ⇒ (x - h)² + (y - k)² = (10)²

Substitute the x and y coordinate in the formula;

• ⇒ [x - (-4)]² + [y - (-9)]² = (10)² [x coordinate (h): -4; y coordinate (k): -9]

• ⇒ [x + 4]² + [y + 9]² = 100 (Option D)

Therefore, Option D is correct.

Answer 2

(x+4)² + (y+9)² = 100

Explanation:

We want to find the equation of a circle with a radius of length 10 and a center at (-4, -9).

general equation of circle : (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

the center is at (-4,-9) so h = -4 and k = -9 and the circle has a radius of 10 so r = 10

so we have (x-h)² + (y-k)² = r²

h = -4 , k = -9 and r = 10

(x-(-4))² + (y-(-9))² = 10²

==> apply double negative sign rule and remove parenthesis for -(-4) and -(-9)

(x+4)² + (y+9)² = 10²

==> simplify exponent

(x+4)² + (y+9)² = 100

and we are done!