Question

For #36, why is the answer 4? Plz explain.

Answer 1

I am getting 7 as the value of b. I do not believe 4 is a correct answer!

Here's why:

General equation of a circle in the xy plane

`(x-c_x)^2+(y-x_y)^2=r^2`

with
`c_x\,\,\mbox{and}\,\,c_y` being the x,y coordinates of the center.

The center point can be determined from the two endpoints of the diameter because the line segment is horizontal, so we just find the center of the x coordinates of the two points:

`c_x = -2+(|8-(-2)|)/(2)=3\\c_y = 3`

and the radius r = diameter/2 = 8-(-2)/2 = 5

so we have

`(x-3)^2+(y-3)^2=5^2`

Given a point on the circle (0,b) with b>0:

`(0-3)^2+(b-3)^2=5^2\\9+(b-3)^2 = 25\\(b-3)^2 = 16\\b=7`