Question

Determine whether the statement is true or false. The circle (x − 1)^2 + (y + 1)^2 = 9 intersects the y−axis.

Answer 1

From that equation we know the center is: (1,-1) and the radius is three.  Since the distance from the center to (0,0) is:

d^2=1^2+1^2

d^2=2

d=√2

Since d<r, √2<3, the circle intersects the y-axis two times.

So the statement saying that the circle intersects the y-axis is true.