MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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: rThen, for the circle P you have:Center: (-4,-7)Radius: 4And for the circle Q:Center: (-2, 3)Radius: 55. 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).