Try this set of practice questions below before you take the graded quiz for this lesson. If you don't do well on the self-check, review this lesson and try again. If you're still having difficulty, contact your teacher for additional help.
1. Identify the equation of a circle with center (2,-11) and radius 3.
- \(\mathsf{(x+2)^2 + (y-11)^2 = 9}\)
- \(\mathsf{(x-2)^2 + (y-11)^2 = 9}\)
- \(\mathsf{(x-2)^2 + (y+11)^2 = 9}\)
- \(\mathsf{(x+2)^2 + (y+11)^2 = 9}\)
If h = 2, k=-11, and r=3, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
If h = 2, k=-11, and r=3, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
If h = 2, k=-11, and r=3, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
If h = 2, k=-11, and r=3, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
2. Identify the equation of a circle with center (-4,2) and diameter 2
- \(\mathsf{(x+4)^2 + (y-2)^2 = 4}\)
- \(\mathsf{(x-4)^2 + (y+2)^2 = 2}\)
- \(\mathsf{(x+4)^2 + (y-2)^2 = 1}\)
- \(\mathsf{(x-4)^2 + (y+2)^2 = 4}\)
If h =-4, k =2, and r =1/2 the given diameter, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
If h =-4, k =2, and r =1/2 the given diameter, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
If h =-4, k =2, and r =1/2 the given diameter, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
If h =-4, k =2, and r =1/2 the given diameter, substitute these values in the general equation of the circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
3. Find the coordinates of the center and the measure of the radius for the circle whose equation is \(\mathsf{ (x+\frac{1}{2})^{2} + (y + \frac{1}{3})^{2} = \frac{16}{25} }\)
- center = \(\mathsf{(\frac12, \frac13)}\) radius = \(\mathsf{\frac45}\)
- center =\(\mathsf{(-\frac12, -\frac13)}\) radius = \(\mathsf{\frac45}\)
- center =\(\mathsf{(-\frac12, \frac13)}\) radius = \(\mathsf{\frac{16}{25}}\)
- center =\(\mathsf{(-\frac12, -\frac13)}\) radius = \(\mathsf{\frac{16}{25}}\)
Refer to the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) to identify h, k, and r.
Refer to the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) to identify h, k, and r.
Refer to the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) to identify h, k, and r.
Refer to the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) to identify h, k, and r.
4. Write the equation of the circle whose graph is shown.
- \(\mathsf{(x-7)^2 + (y-3)^2 = 4}\)
- \(\mathsf{ (x-7)^2 + (y+3)^2 = 4}\)
- \(\mathsf{(x+7)^2 + (y+3)^2 = 2}\)
- \(\mathsf{(x-7)^2 + (y-3)^2 = 2}\)
Read the graph to determine the center (h,k). Count the units on the graph to find the measure of the radius r. Substitute each value in the general equation for a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
Read the graph to determine the center (h,k). Count the units on the graph to find the measure of the radius r. Substitute each value in the general equation for a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
Read the graph to determine the center (h,k). Count the units on the graph to find the measure of the radius r. Substitute each value in the general equation for a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
Read the graph to determine the center (h,k). Count the units on the graph to find the measure of the radius r. Substitute each value in the general equation for a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\)
5. Find the radius of a circle whose center is (-7,-5) if one point on the circle is (-8,-6).
- 1
- \(\mathsf{\sqrt2}\)
- 2
- \(\mathsf{\sqrt12}\)
Evaluate r by substituting the given coordinates in the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) or, since r is the distance from the center to a point in the circle, subsitute the given coordinates in the distance formula \(\mathsf{\sqrt{{ (x_2 - x_1)^2} +{ (y_2 - y_1)^2 }}}\) = d.
Evaluate r by substituting the given coordinates in the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) or, since r is the distance from the center to a point in the circle, subsitute the given coordinates in the distance formula \(\mathsf{\sqrt{{ (x_2 - x_1)^2} +{ (y_2 - y_1)^2 }}}\) = d.
Evaluate r by substituting the given coordinates in the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) or, since r is the distance from the center to a point in the circle, subsitute the given coordinates in the distance formula \(\mathsf{\sqrt{{ (x_2 - x_1)^2} +{ (y_2 - y_1)^2 }}}\) = d.
Evaluate r by substituting the given coordinates in the general equation of a circle \(\mathsf{(x-h)^2 + (y-k)^2 = r^2}\) or, since r is the distance from the center to a point in the circle, subsitute the given coordinates in the distance formula \(\mathsf{\sqrt{{ (x_2 - x_1)^2} +{ (y_2 - y_1)^2 }}}\) = d.
Summary
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