Find an equation of the circle and sketch it if it has: Center on y=4, tangent x-axis at (–2, 0)

OK, lets start by drawing a basic graph (the first one) so we can visualize.

We already know that the y coordinate of the circle's center is .

We know that the circle is tangent to the axis at

That means the x coordinate of the center has to be , as the tangent is a point on the edge of the circle that touches a line at exactly one point.

The radius is the distance from the center of the circle to its edge. We know the center's location now, it is and a point on the edge of the circle (the tangent point) which is . so the distance between the points is 4 which is the radius (you can use the distance formula, but it's quite oblivious.)

We can imagine the circle should look like this (the second one):

Now we can piece together an equation

The equation of a circle is where is the center and is the radius. When we put the numbers in: we get which can be simplified into which is the answer.

Step-by-step explanation: