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1: Plans to build a park include a circular fountain. The outline of the fountain can be modeled with the equation (x-4)^2+(y+5)^2=50, where the units are meters and the graph is on a grid map of the park. Find the coordinates of the center of the fountain AND find the circumference of the fountain.
The center is at (4,-5)
The radius = sqrt(50) = 5sqrt(2)
Circum = 2(pi)r = 2(pi)5sqrt(2) = 10(pi)sqrt(2)
2: Bill is making a graphic design on the computer using a coordinate grid. He starts with a circle with center (0,0). He then draws a congruent circle with the equation x^2+y^2+12x+4y+5=0. What was the radius of the first circle and what translation did he make to draw the second circle?
Complete the square:
x^2+12x+a + y^2+4y+b = -5+a+b
x^2+12x+36 + y^2+4y+4 = -5+36+4
(x+6) + (y+2) = 35
Center at (-6,-2); radius = sqrt(35)
Radius of the 1st circle was sqrt(35)
Translation: He moved the 1st circle 6 to the left
and 2 down.