Question

What is an equation of the circle with center (-5,4) and a radius of 7?

Answer 1

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.