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# Identify the center & radius

0
279
2
+460

1) x+ y2 + 24x + 10y + 160 = 0

2) x2 + y2 - 6x + 10y = 97

3) x2 + y2 +26x + 28y = -364

May 16, 2018

#1
+101228
+2

We need to  complete the square on x and y for each one of these.....you should review how to do this if you are unsure of the procedure....I'll do the first one in some depth

1) x^2 + y^2 + 24x + 10y + 160 = 0

x^2 + 24x +  y^2 + 10y  = -160

Take 1/2 of 24, square it = 12^2  = 144...add to both sides

Take 1/2  of 10, square it  = 5^2  = 25....add to both sides

x^2 + 24x + 144  + y^2 + 10y + 25  = -160 + 144 + 25  factor and simplify

(x + 12)^2  + ( y + 5)^2  = 9

The center is  ( -12, -5)  and the radius  = 3

2) x^2 + y^2 - 6x + 10y = 97

x^2 - 6x + 9  + y^2 + 10y  + 25  =  97  + 9 + 25

(x - 3)^2  + ( y + 5)^2  = 131

The center is  ( 3, -5)  and the radius  is √131

3) x^2 + y^2 +26x + 28y = -364

x^2 + 26x + 169  + y^2 + 28y + 196  = -364 + 169  + 196

(x + 13)^2  + ( y + 14)^2  =  1

The center is  (-13, -14)  and the radius  is 1

May 16, 2018
#2
+460
+1

Ah, thanks. I do remember completing the square.

ZZZZZZ  May 16, 2018