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What is an equation of the circle with center (-5,4) and a radius of 7?
(1) (x - 5)² + (y + 4)² = 14
(2) (x - 5)2 + (y + 4)² = 49
(3) (x + 5)² + (y — 4)² = 14
(4) (x + 5)² + (y - 4)² = 49

Respuesta :

Answer:

Option D

Step-by-step explanation:

Given:

  • Center point: (-5, 4)
  • Radius: 7

Formula:

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

[Where (h, k) is the center point and "r" is the radius of the circle]

Substitute the coordinates of the center point in the formula:

Given center point: (-5, 4)

∴ x-coordinate of center point (h) = -5; y-coordinate of center point (k) = 4

  • ⇒ (x - h)² + (y - k)² = r²
  • ⇒ [x - (-5)]² + [y - 4]² = r²

Substitute the radius in the formula:

Given radius: 7

  • ⇒ [x - (-5)]² + [y - 4]² = r²
  • ⇒ [x - (-5)]² + [y - 4]² = (7)²

Simplify both sides of the equation:

  • ⇒ [x + 5]² + [y - 4]² = (7)(7)
  • ⇒ [x + 5]² + [y - 4]² = 49  (Option D)

Therefore, Option 4 is correct.

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