In the standard x, y plane, a circle has a radius 6 and center (7, 3). the circle intersects the x-axis at (a, 0) and (b, 0). what is the value of a + b?

 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.

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral