Question

Find the equation of a circle with the center within y=x, tangent to y=5, and has a radius 2.

Answer 1

There are two such circles :(

Answer 2

If they're tangent to y=5, and have radius 2, then their y-coordinate is either 3, or 7. The corresponding x-coordinates for these are 3, and 7 respectively.

Answer 3

it's 3 or 7 for the x coordinate of the point of tangency?

Answer 4

The centre of the circle is at either (3, 3), or (7, 7).

Answer 5

How did you get that though?

Answer 6

If the circle is tangent to y=5, then the distance from that line to the centre of the circle is one radius away from the tangent. The tangent line is a horizontal line, so the radius that connects to the tangent is vertical.

The centre of the circle is thus 2 units away from the tangent line in the y-direction. (i.e. 3, or 7). Since the centre of the circle is on the line y=x, then the x-coordinates are (3,3), and (7,7) respectively.