Mark H. answered • 10/06/19

Tutoring in Math and Science at all levels

the general procedure:

The standard form is (x + a)^{2} + (y - b)^{2} = r^{2}

r is the radius, and a and b are the x and y offsets

the trick is simply to plug in known values to get one or more equations. (You need the same number of equations as you have unknowns)

__Always start by plotting the given information on graph paper __

**a)****With center (0, 5); passes through (0, 0):**

From this, we know that the radius is 5 (the given point is at the same x-value, and they are 5 units apart on the y-axis). We can then see that the circle passes through (0,10), and also (-5,5) and (5,5).

Since the center is at y = 5, the y offset is -5. So our equation is:

(x + 0)^{2} + (y - 5)^{2} = 5^{2}

__x__^{2}__ + (y - 5)__^{2}__ = 25__

**b)****Radius 4, tangent to x-axis; contain (–5,8):**

If the circle has the x=axis as a tangent, then all of it is either above or below the x-axis. Since the radius is 4, the top of the circle will be at +8, OR: the bottom will be at -8

__Make a plot to see this!!__

We are given the point (-5,8). Since the y-value is +8, we now know that the circle is above the x=axis. With the given value of x = -5, we know that the vertical centerline is at x = -5, and therefor, the center is at (-5,4)

__Use the plot!!__

So-----the equation is (x + 5)^{2} + (y - 4)^{2} = 16

Ted B.

Thanks!!!10/06/19