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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.

Mar 23, 2019

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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)

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.   