4.4b: Equations of a Circle p of%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 Primary M(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 circle (x-h) 2 + (y-k) 2 = r 2 r = radius length (h,k) = coordinates of the center point (x,y) represents the ordered pairs for every point on the circle.

Ex: Write the standard equation of a circle with center (-5,0) and a radius of 4.8. (x-h) 2 + (y-k) 2 = r 2 (x-(-5)) 2 + (y-0) 2 = (x+5) 2 + y 2 = 4.8 2

The point (2,1) is on a circle whose center is (4,-3). Write the standard equation of the circle. We need the radius length. Use distance formula from center to the pt. on the circle to find the radius. (x-h) 2 + (y-k) 2 = r 2 (x-4) 2 + (y-(-3)) 2 = (x-4) 2 + (y+3) 2 = 20

Ex: Graph the circle denoted by the equation (x-3) 2 + (y+1) 2 = 4. Center?(3,-1)Radius? r = = 2 To graph: * Graph the center pt. 1 st. * Use radius length to get 4 pts. on the circle. (one above, below, to left & right) * Do your best to draw a circle thru those 4 pts.

Write the equation In standard form Of this circle

Write the equation In standard form Of this circle

Assignment