Do Now Write the equation for the locus of points 5 units from the point (-5,6)

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Presentation transcript:

Do Now Write the equation for the locus of points 5 units from the point (-5,6)

The Circle Aim : What are the standard and general forms of the equation of a circle?

Applications The Circle: WHEELS

AND TABLE TOPS

Definition The circle is the locus (set) of all points that are equidistant from a given point called the center. Center ( h,k ) Radius P( x,y )

Definition The standard form of the equation of a circle with radius r and center at ( h,k ) is:

Solution to Do Now h =-5 k =6 (-5,6)

Try This Graph the circle with center at (-2,-1) and radius 2 using a graphing calculator...

Steps: 1. Write equation in standard form. 2. Solve for y 3. Enter in calculator: y 1 & y 2 4. Set window

Solution... Window x [-6.4, 3] By y [-4, 2]

Definition The general form of the equation of a circle is: Where a, b, and c are constant

Try This Write the equation of the circle with center at (-5,6) and radius of 5 in general form

The equation of a circle is: Write the equation in standard form. Find the radius and coordinates of the center. Hint: Change to standard form by completing the square

Try This The equation of a circle is: Find the radius and coordinates of the center. Radius=0.5 ; Center: (3,-2)

Also Try This is a circle with radius 7. Find the value of k. k = – 8

A(–1,6) and B(3,–2) are endpoints of a diameter of a circle a)Write an equation of this circle b) What are the coordinates of the y-intercepts of this circle?

Solution y = –2.359 y = 6.359