D LIO ps) T he points A(3,9) and B(7,11) are the endpoints of a diameter of a ci
ID: 3019359 • Letter: D
Question
D LIO ps) T he points A(3,9) and B(7,11) are the endpoints of a diameter of a circle a) Find the center of the circle b) Find the radius of the circle. c) Find the equation of the circle. d) What two equations would you type into your graphing calculator to graph the top half and the bottom half of the circle as separate functions? e) Algebraically or graphically determine where the line y 15 -x meets the circle. g) Draw a graph of the circle, the line, and the following 5 points: the center, the 2 original points, and the 2 points of intersection. Label each point with its x and y coordinates.Explanation / Answer
A(3,9), B(7,11)
Mid point of AB= ((3+7)/2 , ( 9+11)/2) = (5, 10)
a . Center= (5,10)
Diameter= sqrt((7-3)2+ (11-9)2) = sqrt(16+4) = sqrt 20 = 2sqrt5
b . radius = diameter/2 = 2sqrt5/2= sqrt5
c . Equation of circle
(x-h)2+(y-k)2=r2
(x-5)2+ (y-10)2= 5
d. (y-10) = sqrt(5 - (x-5)^2) for upper half
(y-10) =- sqrt( 5 - (x-5)2) for lower half
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