Question

Circle P is described by the equation (×+4)2 +(y+7)2=16 and circle Q is described by the equation (x+2)2 + (y-3)2 =25. Select from the drop_down menus to correctly complete the statements. Circle Q is .........units to the .........of circle P and ..........units........it. Circle Q has ..........circle P. A) 2, 4, 6 or 10. B) Left or right. C) 2,4,6,or 10. D) above or below. E) A shorter radies than, The same radius as, A longer radius than?

Answer 1

Circle Q is 2 units to the right of circle P and 10 units above it. Circle Q has a longer radius than circle P.

Step-by-step explanation:

1. Circle P:

• 
  `(x+4)^2+(y+7)^2=16`

2. Circle Q:

• 
  `(x+2)^2 + (y-3)^2 =25`

3. Using the general form of the canonic equations, you can tell inmediately the coordinates of the center and the radius of each circle:

• 
  `(x-a)^2+(y-b)^2=r^2`

• Center: (a,b)

• Radius: r

Then, for the circle P you have:

• Center: (-4,-7)

• Radius: 4

And for the circle Q:

• Center: (-2, 3)

• Radius: 5

5. Then, to complete statements you have:

• Circle Q is: -2 - (-4) = - 2 + 4 = 2 units to the right of Circle P.

• Circle Q is: 3 - (-7) = 3 + 7 = 10 units above circle P

• Circle Q has longer radius (5) than circle P (4).