Final answer:
The standard form of the equation of the circle with radius 7 and center (4, -9) is (x - 4)² + (y + 9)² = 49.
Step-by-step explanation:
To write the standard form of the equation of a circle with a given radius and center, you can use the general equation of a circle which is:
(x - h)² + (y - k)² = r²
Here, (h, k) represents the coordinates of the center of the circle, and r is the radius of the circle.
In this case, the center of the circle is given as (4, -9) and the radius is 7. Plugging these values into the general equation, we get:
(x - 4)² + (y + 9)² = 7²
Next, we simplify the equation by squaring the radius:
(x - 4)² + (y + 9)² = 49
This is the standard form of the equation for the circle with radius 7 and center at (4, -9).