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# Geometry

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680
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The equation for the circle is:

x2+y2−12x+6y−19=0x2+y2−12x+6y−19=0 .

What is the center of the circle?

(-6, 3)

(12, -6)

(6, -3)

(-12, 6)

The equation x2 + (y + 3)2 = 36 models the boundary on a local map for which Darren can hear his friend Tom on his two-way radio when Darren is at home. How far (in miles) can Tom walk from Darren's home and still be heard?

3 miles

6 miles

2 miles

12 miles

May 3, 2017

### Best Answer

#1
+3

1.

I think this is the equation for the circle:

x2 + y2 − 12x + 6y − 19 = 0

Add 19 to both sides and rearrange the terms.

x2 − 12x + y2 + 6y = 19

Add (12/2)2 = 36  and  (6/2)2 = 9 to both sides.

x2 - 12x + 36 + y2 + 6y + 9 = 19 + 36 + 9

Factor the left side.

(x - 6)(x - 6) + (y + 3)(y + 3) = 64

(x - 6)2 + (y + 3)2 = 64

Now that the equation is in this format, we can see that the center of the circle is located at (6, -3)

2.

This is the equation of a circle:

x2 + (y + 3)2 = 36

Darren can hear Tom as long as Tom stays within the radius of that circle.

The radius of that circle = $$\sqrt{36}$$ = 6 miles

May 4, 2017

### 1+0 Answers

#1
+3
Best Answer

1.

I think this is the equation for the circle:

x2 + y2 − 12x + 6y − 19 = 0

Add 19 to both sides and rearrange the terms.

x2 − 12x + y2 + 6y = 19

Add (12/2)2 = 36  and  (6/2)2 = 9 to both sides.

x2 - 12x + 36 + y2 + 6y + 9 = 19 + 36 + 9

Factor the left side.

(x - 6)(x - 6) + (y + 3)(y + 3) = 64

(x - 6)2 + (y + 3)2 = 64

Now that the equation is in this format, we can see that the center of the circle is located at (6, -3)

2.

This is the equation of a circle:

x2 + (y + 3)2 = 36

Darren can hear Tom as long as Tom stays within the radius of that circle.

The radius of that circle = $$\sqrt{36}$$ = 6 miles

hectictar May 4, 2017