1) Write the equations of the following circles.
a) center \((-3, 7)\) and radius \(4\sqrt3\)
b) center \((4, -2)\) and point on circle \((6, 11)\)
c) endpoints of a diameter of the circle \((-1, 9)\) and \((5, 1)\)
2) Given the circle with equation \((x + 7)^2 + (y – 5)^2 = 72\)
a) Find the center and radius.
b) Find the circumference.
c) Find the area.
3) Find the center and radius of the circle represented by each equation:
a) \(x^2 + 7x + y^2 – 5y = -1\)
b) \(6x^2 – 12x + 6y^2 + 24y = 42\)
c) \(4x^2 + 4y^2 + 20x – 12y = 6\)
4) Write the equation in standard form and find the location of the center and length of the radius.
a) \(x^{2} - 9x + y^{2} - \dfrac{19}{4}y = 0\)
b) \(x^{2} + y^{2} + 7x - \dfrac{3}{4}y = \dfrac{51}{16}\)
5) Find the center of a circle that passes through the following points:
a) \(A(0, 0), B(6, -4)\), and \(C(2, -10)\).
b) \(A(3, 5), B(6, -4)\), and \(C(0, 8)\).
6) What is the value of \(c\) in the equation so that the circle has a radius of \(11\)?
\(x^2 + y^2 -4x + 4y + c = 0\)
7) Given the circles represented by \(x^2 + 8x + y^2 = 9\) and \(x^2 + y^2 – 16y = -15\), find the length of the common external tangent.
8) Determine the equation of the circle with a center at \((-4, 11)\) and tangent to the line \(3x + 7y = 7\).
9) Given circles \(x^2 + y^2 - 16x +6y + 64 = 0\) and \(x^2 + y^2 - 6x + 6y - 46 = 0\). Determine the point(s) of intersection of the two circles.
Solution Bank
a) center \((-3, 7)\) and radius \(4\sqrt3\)
b) center \((4, -2)\) and point on circle \((6, 11)\)
c) endpoints of a diameter of the circle \((-1, 9)\) and \((5, 1)\)
2) Given the circle with equation \((x + 7)^2 + (y – 5)^2 = 72\)
a) Find the center and radius.
b) Find the circumference.
c) Find the area.
3) Find the center and radius of the circle represented by each equation:
a) \(x^2 + 7x + y^2 – 5y = -1\)
b) \(6x^2 – 12x + 6y^2 + 24y = 42\)
c) \(4x^2 + 4y^2 + 20x – 12y = 6\)
4) Write the equation in standard form and find the location of the center and length of the radius.
a) \(x^{2} - 9x + y^{2} - \dfrac{19}{4}y = 0\)
b) \(x^{2} + y^{2} + 7x - \dfrac{3}{4}y = \dfrac{51}{16}\)
5) Find the center of a circle that passes through the following points:
a) \(A(0, 0), B(6, -4)\), and \(C(2, -10)\).
b) \(A(3, 5), B(6, -4)\), and \(C(0, 8)\).
6) What is the value of \(c\) in the equation so that the circle has a radius of \(11\)?
\(x^2 + y^2 -4x + 4y + c = 0\)
7) Given the circles represented by \(x^2 + 8x + y^2 = 9\) and \(x^2 + y^2 – 16y = -15\), find the length of the common external tangent.
8) Determine the equation of the circle with a center at \((-4, 11)\) and tangent to the line \(3x + 7y = 7\).
9) Given circles \(x^2 + y^2 - 16x +6y + 64 = 0\) and \(x^2 + y^2 - 6x + 6y - 46 = 0\). Determine the point(s) of intersection of the two circles.
Solution Bank