Distance and Circles

Distance and Circles Standard form for the equation of a circle : ( h , k ) r • - center ( h , k ) • radius ( r )

Distance and Circles Standard form for the equation of a circle : ( h , k ) r • - center ( h , k ) • radius ( r ) The distance from the center of the circle to any point ( x , y ) ON the circle is the RADIUS

Distance and Circles Standard form for the equation of a circle : ( h , k ) r - center ( h , k ) - radius ( r ) When the equation of the circle is given in the form; You must rewrite the equation in standard form by completing the square…

Distance and Circles Standard form for the equation of a circle : ( h , k ) r - center ( h , k ) - radius ( r ) When the equation of the circle is given in the form; You must rewrite the equation in standard form by completing the square… Let’s look at the standard form first…

Distance and Circles Find the center and radius of the circle whose equations is : ( h , k ) r

Distance and Circles Find the center and radius of the circle whose equations is : ( h , k ) To get ( x – 4 ), h would have to be +4 - ( x – h )2 = ( x – (+4))2 = (x – 4 )2 r

Distance and Circles Find the center and radius of the circle whose equations is : ( h , k ) To get ( x – 4 ), h would have to be +4 - ( x – h )2 = ( x – (+4))2 = (x – 4 )2 To get ( y + 3 ), k would have to be - 3 - ( y – k )2 = ( y – ( -3))2 = ( y + 3 )2 r

Distance and Circles Find the center and radius of the circle whose equations is : ( h , k ) To get ( x – 4 ), h would have to be +4 - ( x – h )2 = ( x – (+4))2 = (x – 4 )2 To get ( y + 3 ), k would have to be - 3 - ( y – k )2 = ( y – ( -3))2 = ( y + 3 )2 CENTER = ( 4 , - 3 ) r

Distance and Circles Find the center and radius of the circle whose equations is : ( h , k ) To get ( x – 4 ), h would have to be +4 - ( x – h )2 = ( x – (+4))2 = (x – 4 )2 To get ( y + 3 ), k would have to be - 3 - ( y – k )2 = ( y – ( -3))2 = ( y + 3 )2 There is a shortcut…just use the OPPOSITE sign you see in front of h and k r CENTER = ( 4 , - 3 )

Distance and Circles Find the center and radius of the circle whose equations is : ( h , k ) To get ( x – 4 ), h would have to be +4 - ( x – h )2 = ( x – (+4))2 = (x – 4 )2 To get ( y + 3 ), k would have to be - 3 - ( y – k )2 = ( y – ( -3))2 = ( y + 3 )2 There is a shortcut…just use the OPPOSITE sign you see in front of h and k r CENTER = ( 4 , - 3 ) and if r2 = 36, r = 6

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation :

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Rewrite the equation getting your x’s and y’s together.

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Rewrite the equation getting your x’s and y’s together. Move any integer to the other side of the equation.

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Rewrite the equation getting your x’s and y’s together. Move any integer to the other side of the equation. Leave one blank space behind each x/y group and 2 behind your #

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Write the standard equation form leaving blanks in the spots in squares… also leave a few lines space for the next step in between…

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : To complete the square, divide the linear x and y coefficient by 2…

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : To complete the square, divide the linear x and y coefficient by 2…the answer will fill in the blank spaces in the standard form…

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Next, square those answers and fill in the blank spaces on both sides of the equation…

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Then, complete the addition on the right side and fill in the the last blank in the standard form…

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation :

Distance and Circles Completing the square – forcing an expression into a perfect square trinomial EXAMPLE : Find the center and radius of a circle defined by the equation : Center = ( - 8 , - 5 ) r = 3

Distance and Circles