AnalysisBCName:______
Miss Hall
Circle Worksheet
Write equations in standard form , unless otherwise noted.
1. Find the equations of all circles that…
a. Have the segment AB with A(-2, -4) and B(6, 4) as a diameter.
b. Pass thru A(3, 0) and B(12, 0) and are tangent to the y-axis.
c. Have centers on the line , and are tangent to both axes.
d. Pass thru A(3, 6) and B(-4, -1) and have centers on the y-axis.
e. Have centers at P(8, 4) and are tangent to the line whose intercepts are (6, 0) and (0, 3).
2. Find the general form of the equation of the locus of all points which are three times as far from the point (-4, 2) as from the point (8, 6).
3. Find an equation that represents the family of all circles with center on the line that pass thru the origin. Find the particular member that passes thru (6, 2).
4. Find the equation of the circle that passes thru the 3 points…
a. (6, 10), (0, 2), and (2, 8)b. (1, -1), (2, 6), (-5, -1)
5. Find the equation of the circle with center at (5, -3) that is tangent to the line .
6. Find the equation of the circle that has its center on the y-axis and is tangent to the line at the point (2, 2).
7. Find the equation of the circle that is tangent to the line at the point (-1, -2) and passes thru the point (6, -1).
Answers!
1a.
1b.
1c. ,
1d.
1e.
2.
3. ,
4a.
4b.
5.
6.
7. (Hint: use the 2 points on the circle to get 2 expressions for the radius in terms of h and k, then set them equal to each other to get k in terms of h, and use the slope: the line between (-1, -2) and the center (h, k) is perpendicular to the given line.)