What equation represents a circle with a center at (-4,9) and a diameter or 10 units

(x + 4) ² + (y - 9) ² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h) ² + (y - k) ² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = ( - 4, 9) and r = 10 : 2 = 5, thus

(x - ( - 4)) ² + (y - 9) ² = 5², that is

(x + 4) ² + (y - 9) ² = 25 ← equation of circle