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anonymous
 one year ago
fan/medal to first person to help/answer
Using the following equation, find the center and radius:
x2  4x + y2 + 8y = 4 (5 points)
The center is located at (2, 4), and the radius is 4.
The center is located at (2, 4), and the radius is 4.
The center is located at (2, 4), and the radius is 16.
The center is located at (2, 4), and the radius is 16.
anonymous
 one year ago
fan/medal to first person to help/answer Using the following equation, find the center and radius: x2  4x + y2 + 8y = 4 (5 points) The center is located at (2, 4), and the radius is 4. The center is located at (2, 4), and the radius is 4. The center is located at (2, 4), and the radius is 16. The center is located at (2, 4), and the radius is 16.

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campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1well the general form of the circle you need is \[(x  h)^2 + (y  k)^2 = r^2\] so you need to complete the square in both x and y... can you do that..?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what does k stand for and how do I find the height in the eqaution?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1(h, k) is the centre of the circle and r is the radius

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so I need to find x first?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1no you have \[x^2  4x \] you need to add a value so it forms a perfect square e.g.\[(x  a)^2 = x^2 2ax + a^2 \] this is called completing the square.. ay thoughts...

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1so you need to compare 2ax and 4x any thoughts on the value of a...?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1great so 2^2 = 4 so add 4 to both sides of the equation to keep it in balance. now the equation can be written as \[(x  2)^2 +y^2 + 8y = 0\] next complete the square in y... \[(y + a)^2 =y^2 + 2ay + a^2 \] so compare 2ay with 8y what is the value of a..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1yes... so 4^2 = 16 again add 16 to both sides of the equation... and you get \[(x 2)^2 + (y + 4)^2 = 16\] now you can identify the radius and centre

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1the expanded form of the equation, just to check is \[x^2  4x + 4 + y^2 _ 8y + 16 = 16 ~~or ~~x62 4x + y^2 + 8y + 20 = 16\] subtract 20 from both sides of the equation and you get \[x^2 4x + y^2 + 8y = 4\] the original equation

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1no it's not... remember the equation is \[(x  h)^2 + (y  k)^2 = r^2\] (h, k) is the centre r is the radius... so take the square root to find r

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1the centre is correct..

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1that's correct now you have all the information you need

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so B is the correct answer correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i would fsn u but i already am
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