Graphing a Circle: Find Center, Radius & Intercepts

In summary, to find the center of a circle using a graph, locate the coordinates of the center point (usually denoted by h and k) by counting units from the origin or using the equation (h,k). The radius of a circle is the distance from the center point to any point on the circumference, denoted by r. To find the radius using a graph, measure the distance or use the equation r = √(x-h)² + (y-k)². To graph a circle with given center and radius, plot the center point and draw a circle with the given radius. The x and y intercepts of a circle can be found by looking for the points where the circle intersects the axes or solving the equation
  • #1
elitespart
95
0
Consider x^2 + y^2 – x + 2y + 1 = 0.
(a) Find the coordinates of the center and the length of the radius.
(b) Determine the coordinates of the intercepts.
(c) Graph the circle.



I'm really lost on this one. I tried plugging in numbers but I seriously doubt that's how I'm supposed to do it. Can someone point me in the right direction? Thanks
 
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  • #2
Standard Form versus General Form.
Completing the Square.
 
  • #3
oh so just (x-1/2)^2 + (y+1)^2 = 1/4? center would be at (1/2, -1) and radius is sqrt(1/4)=(1/2)?
 
  • #4
elitespart said:
oh so just (x-1/2)^2 + (y+1)^2 = 1/4? center would be at (1/2, -1) and radius is sqrt(1/4)=(1/2)?

Yup! :biggrin:
 

1. How do I find the center of a circle using a graph?

To find the center of a circle using a graph, you will need to locate the coordinates of the center point. This can be done by looking at the x and y values of the center point, which are usually denoted by the letters h and k. These values can be found by counting the number of units from the origin, or by using the equation (h,k).

2. What is the radius of a circle and how do I find it using a graph?

The radius of a circle is the distance from the center point to any point on the circle's circumference. This distance is usually denoted by the letter r. To find the radius using a graph, you can measure the distance from the center point to any point on the circle's circumference using a ruler or by counting the number of units. Alternatively, you can use the equation r = √(x-h)² + (y-k)², where (h,k) is the center point and (x,y) is any point on the circle's circumference.

3. How do I graph a circle when given the center and radius?

To graph a circle when given the center and radius, start by plotting the center point on the graph. Then, using a compass or a ruler, draw a circle around the center point with a radius equal to the given value. Make sure to label the circle with the center point and the radius. Alternatively, you can use the equation (x-h)² + (y-k)² = r², where (h,k) is the center point and r is the radius, to plot multiple points on the circle and connect them to form the shape.

4. How do I find the x and y intercepts of a circle using a graph?

The x intercept of a circle is the point where the circle intersects the x-axis, and the y intercept is the point where the circle intersects the y-axis. To find these intercepts using a graph, you can look for the points where the circle crosses these axes. Alternatively, you can set either the x or y value in the equation (x-h)² + (y-k)² = r² to 0, and solve for the other variable to find the intercepts.

5. Can a circle have more than one center and radius?

No, a circle can only have one center and one radius. The center is the unique point from which all points on the circle are equidistant, and the radius is the unique distance from the center to any point on the circle's circumference. If a circle appears to have multiple centers or radii, it is likely an ellipse or another type of curved shape, not a circle.

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