+0

# Geometry

0
265
1

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

Guest May 3, 2017

#1
+6356
+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

hectictar  May 4, 2017
Sort:

#1
+6356
+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

hectictar  May 4, 2017

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details