Final answer:
The possible values for b for the point (2,b) that lies on the circle with center (-1,-2) and radius 7 are approximately 4.32 and -8.32 when calculated using the equation of a circle.
Step-by-step explanation:
To find the possible values of b for the point (2,b) that lies on the circle with center (-1,-2) and a radius of 7, we use the equation of a circle in standard form:
(x - h)^2 + (y - k)^2 = r^2
For a circle with center (h,k) and radius r, the corresponding values are h = -1, k = -2, and r = 7. Substituting these values and the x-coordinate of the point (2,b) into the equation gives:
(2 - (-1))^2 + (b - (-2))^2 = 7^2
Solving this, we get:
3^2 + (b + 2)^2 = 49
9 + (b + 2)^2 = 49
(b + 2)^2 = 40
b + 2 = ±5√40
b = -2 ± √40
So the possible values for b are approximately -2 + 6.32 and -2 - 6.32, which are about 4.32 and -8.32, respectively.