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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?

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Edufirst

Answer:

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.

Explanation:

1. Circle P:

  • [tex](x+4)^2+(y+7)^2=16[/tex]

2. Circle Q:

  • [tex](x+2)^2 + (y-3)^2 =25[/tex]

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

  • [tex](x-a)^2+(y-b)^2=r^2[/tex]

  • 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).

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