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
+9481 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
+9481 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
