4.4b: Equations of a Circle4.4b: Equations of a Circlep. 498-503p. 498-503

http://guilford.rps205.com/departments/Math/Links/Honors%20Geometry/Honors%20Geometry%20Power%20Points/10.6%20Equations%20of%20Circles.ppt#7

M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. (State)

Secondary

PrimaryM(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

GSE’s

Standard equation of a circleStandard equation of a circle

(x-h)(x-h)22 + (y-k) + (y-k)22 = r = r22

r = radius lengthr = radius length

(h,k) = coordinates of the center point(h,k) = coordinates of the center point

(x,y) represents the ordered pairs for (x,y) represents the ordered pairs for every pointevery point onon the circle. the circle.

ExEx: Write the standard equation of a : Write the standard equation of a circle with center (-5,0) and a radius circle with center (-5,0) and a radius

of 4.8.of 4.8.

(x-h)(x-h)22 + (y-k) + (y-k)22 = r = r22

(x-(-5))(x-(-5))22 + (y-0) + (y-0)22 = 4.8 = 4.822

(x+5)(x+5)22 + y + y22 = 4.8 = 4.822

The point (2,1) is on a circle whose The point (2,1) is on a circle whose center is (4,-3). Write the standard center is (4,-3). Write the standard

equation of the circle.equation of the circle.We need the radius length.We need the radius length.

Use distance formula from center to the Use distance formula from center to the pt. on the circle to find the radius.pt. on the circle to find the radius.

(x-h)(x-h)22 + (y-k) + (y-k)22 = r = r22

(x-4)(x-4)22 + (y-(-3)) + (y-(-3))22 = =

(x-4)(x-4)22 + (y+3) + (y+3)22 = 20 = 20

20r

220

ExEx: Graph the circle denoted by the : Graph the circle denoted by the equation (x-3)equation (x-3)22 + (y+1) + (y+1)22 = 4. = 4.

Center?Center?

(3,-1)(3,-1)

Radius?Radius?

r = = 2r = = 2

To graph:To graph:

* Graph the center pt. 1* Graph the center pt. 1stst..

* Use radius length to * Use radius length to get 4 pts. on the circle. (one get 4 pts. on the circle. (one above, below, to left & right)above, below, to left & right)

* Do your best to draw a * Do your best to draw a circle thru those 4 pts.circle thru those 4 pts.

4

Write the equationIn standard form Of this circle

Write the equationIn standard form Of this circle

Assignment