Circles Formula. x 2 + y 2 = r 2 Formula for Circle centered at the origin Center point (0,0) Radius = r.

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Presentation transcript:

Circles Formula

x 2 + y 2 = r 2 Formula for Circle centered at the origin Center point (0,0) Radius = r

(h,k) (0,0) r r r r r r

Center = (0,0) Radius = 5 Plot the center Count & Plot the radius in 4 directions x 2 + y 2 = 25

(0,0) (0,5) (0,-5) (5,0)(-5,0)

Center = (0,0) Radius = sqrt(15) Plot the center Count & Plot the radius in 4 directions x 2 + y 2 = 15

(3.9,0)(-3.9,0)(0,0) (0,3.9) (0,-3.9)

Center = (2,5) Radius = 2.5 (x-2) 2 +(y-5) 2 = 6.25

Center = (3,3) Radius = 6 (x-3) 2 +(y-3) 2 = 36

Center = (-2,-4) Radius = 11 (x+2) 2 +(y+4) 2 = 121

Center = (-7,1) Radius = 10 (x+7) 2 +(y-1) 2 = 100

x 2 +14x y 2 – 2y +1 = 100 x 2 +14x + y 2 – 2y = 100 – 49 – 1 x 2 +14x + y 2 – 2y = 50 If you expand the equation does it change the shape?

x 2 +4x+y 2 +8y = x 2 +4x+ +y 2 +8y+ = 101 but remember if you add to one side of an equation you must add to the other. x 2 +4x+ +y 2 +8y+ = how do you fill in the blanks to get an equation for a circle? (x – h) 2 + (y – k) 2 = r 2 Can you work backwards?

101x 2 +4x+ +y 2 +8y+ = 101 x 2 +4x+ +y 2 +8y+ = tocan you make the connection from the left side to the right? (x – h) 2 + (y – k) 2 = r 2 (x + 2) 2 + (y + 4) 2 = 121 x 2 +4x+y 2 +8y = CV # 14

circle centered at P(h,k) tangent to L

So what is the process… You have a line and a point… Identify the slope and the perpendicular slope Identify the perpendicular line through the given point Find the point of intersection of the two lines Find the distance between the two points. CV # 9

Pythagorean Theorem a 2 + b 2 = c 2 a 2 = c 2 - b 2 a 2 + b 2 - c 2 = 0

Find the equation of the circle A(4,4) B(-1,-4)

Find the center using the midpoint formula. A(4,4) B(-1,-4)

Find the center using the midpoint formula. A(4,4) B(-1,-4) h = (4+ -1)/2 k = (4+-4)/2 h = 3/2 k = 0/2 h = 1.5 k = 0 center : C(1.5, 0)

Find the radius using the distance formula with one point and the center. A(4,4) B(-1,-4) C(1.5, 0)

Find the radius using the distance formula with one point and the center. A(4,4) B(-1,-4) C(1.5, 0) r = sqrt( ( )^2 + (4 – 0)^2 ) r = sqrt( (2.5)^2 + (4)^2 ) r = sqrt( ) r = sqrt( ) r =

Equation for this circle A(4,4) B(-1,-4) C(1.5, 0) r = sqrt( ( )^2 + (4 – 0)^2 ) r = sqrt( (2.5)^2 + (4)^2 ) r = sqrt( ) r = sqrt( ) r = (x – 1.5)^2 + (y – 0)^2 = ^2 (x – 1.5) 2 + y 2 = 22.25