Answer: The required value of a+b is 14.
Step-by-step explanation: Given that in the standard xy plane, a circle has a radius 6 and center (7, 3).
The circle intersects the x-axis at (a, 0) and (b, 0).
We are to find the value of a+b.
We know that
the standard equation of a circle with center at (h, k) and radius r units is given by
For the given circle, we have
(h, k) = (7, 3) and r = 6 units.
So, from equation (i), we get
Since the circle (ii) passes through the points (a, 0) and (b, 0), so let the point be denoted by (c, 0), then we have
Therefore, we get
That is,
Thus, the required value of a+b is 14.