# Equation of a Circle

The equation of a circle is a fundamental concept in mathematics, providing a concise representation of all points equidistant from a fixed center point. Described by its radius and center coordinates, this equation holds significance across various fields, including geometry, algebra, and physics. By understanding its formulation and properties, one can explore geometric relationships, solve problems in coordinate geometry, and apply it in practical scenarios such as navigation systems and engineering designs. Mastering the equation of a circle lays a solid foundation for deeper mathematical exploration and problem-solving endeavors.

Questions

- Two circles have the following equations: #(x -8 )^2+(y -5 )^2= 64 # and #(x +4 )^2+(y +2 )^2= 25 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- A circle has a center that falls on the line #y = 3x +4 # and passes through #(4 ,4 )# and #(9 ,2 )#. What is the equation of the circle?
- Two circles have the following equations #(x -1 )^2+(y -6 )^2= 64 # and #(x +7 )^2+(y +2 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- What is the equation of the circle with a center at #(5 ,7 )# and a radius of #6 #?
- Two circles have the following equations: #(x -1 )^2+(y -2 )^2= 9 # and #(x +6 )^2+(y +2 )^2= 25 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- What is the equation of the circle with a center at #(3 ,5 )# and a radius of #1 #?
- A circle has a center that falls on the line #y = 3/7x +3 # and passes through # ( 2 ,8 )# and #(3 ,5 )#. What is the equation of the circle?
- What is the equation of a circle with its center at (10, -4) and a radius of 4?
- Two circles have the following equations #(x -1 )^2+(y -7 )^2= 25 # and #(x +3 )^2+(y +3 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- How do you graph #(x-3)^2+y^2=16#?
- What is the equation of the circle with a center at #(2 ,6 )# and a radius of #3 #?
- Find the equation of a circle, which passes through origin and has #x#-intercept as #3# and #y#-intercept as #4#? What would have been the equation, if intercepts are reversed?
- A circle has a center that falls on the line #y = 1/7x +4 # and passes through # ( 7 ,8 )# and #(3 ,6 )#. What is the equation of the circle?
- A circle has a center that falls on the line #y = 3/8x +3 # and passes through # ( 1 ,4 )# and #(2 ,9 )#. What is the equation of the circle?
- How to write standard form of the equation circle with a center of (-1,4);circumference 6pie?
- Two circles have the following equations #(x -1 )^2+(y -4 )^2= 64 # and #(x +3 )^2+(y +1 )^2= 9 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- How do you graph a circle a circle with a center at #(0, -6)# and a radius of 1?
- A circle has its center at (2,2) and is tangent to both the x-axis and y-axis. A line tangent to this circle intersects the x-axis at (a,0) and the y-axis at (0,b). If the shaded area is equal to the area of the circle, then a + b = ? (EXACT ANSWER).
- How do you write an equation of a circle with center at (0,0), d=12?
- A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,5 )# and #(8 ,7 )#. What is the equation of the circle?