Find an equation of the circles:(there are 6 questions)

Question

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

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

c)Center on line x=3, tangent y-axis at (0, 5)

d)With center (–2, 0); passes through (2, 0)

e)Radius 5, tangent to y-axis; contain (10,7)

f)Center on line y–4=0, tangent x-axis at (–2, 0)

PLEASE HELP AND THANK YOU IF YOU DO!!!

Answer 1

the general procedure:

The standard form is (x + a)² + (y - b)² = r²

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 = 5²

x² + (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