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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

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 class=

Sagot :

SenorMathWiz

Answer:

(x+4)² + (y+9)² = 100

Step-by-step 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!

Answer:

Option D

Step-by-step 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.

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