+26 1. The equation of a circle is x²+y²+14x+10y-7=0. You must show all work. If you use DESMOS, you must put the snip of your work.
a. Fill in the blanks: x²+14x+___+y²+10y+___=___
b. What is the equation in Standard Form?
c. What is the center and radius of the circle?
2.
The equation of a circle is (x−11) ²+(y+15) ²=144.
(a) Johnny said that the center of the circle is located at (15, -11). Is Johnny correct? Explain your answer.
(b) Joyce said that the diameter of the circle is 144 units. Is Joyce correct? Explain your answer.
+129849 We are completing the square on x and y
Take 1/2 of 14 = 7, square it =49 add to both sides
Take 1/2 of 10 =5, square it = 25 add to both sides
a. Fill in the blanks: x²+14x+ 49+y²+10y+ 25 = 74
b. Standard Form = ( x + 7)^2 + ( y + 5)^2 = 74
c. Center ( - 7, - 5)
Radius = sqrt (74)
2.
The equation of a circle is (x −11) ²+(y+15) ²=144.
(a) Johnny said that the center of the circle is located at (15, -11). Is Johnny correct? Explain your answer.
In the form ( x - a)^2 + ( y + b)^2 = r^2....the center is ( a, - b).....so....
The center is (11, - 15)
(b) Joyce said that the diameter of the circle is 144 units. Is Joyce correct? Explain your answer.
144 = radius^2
12 = radius
2 * radius = diameter
2 * 12 =
24 = the diameter
