Cirlce in coordinate plane.

Objectives:

• Develop and use the equation of a circle.
• Adjust the equation of the circle to move the center ub a coordinate plane.

The Equation of a Circle:

• Given the definition of a circle: The set of all points in a plane that are equidistant from a given point called the center, we know that we are dealling with points in the coordinate plane that are a given distance, r, from a single point, the center, that we'll call (h,k) so that we can use them anywhere in the plane.
• since we are working with distance the distance formula will be used.
• Replace the letter with the new information we know.
• r= the square root of x-h squared + y - k squared.
• replaceing distance with the word radius.
• Square both sides and you'll get the radius squared=x-h squared + y-k squared
• an equation for a circle at (h,k) and a radius of r units is
• (x-h)squared+(y-k)squared=rsquared.

Key Skills:

Sketch a cirlce from its equation.

(x-2)2+(y-1)2=9