Question

complete the square to find the center and radius of the circle whose equation is x^2 + y^2 + 8x - 4y = 36

Answer 1

@dan815

Answer 2

you need to complete the square in both x and y

\[(x^2 + 8x+ ?) + (y^2 -4y+ ??) = 36\]

the values you add to complete the square need to be added to both sides of the equation.

then factor

the standard form is

\[(x -h)^2 + (y - k)^2 = r^2\]

where (h, k) is the centre and r is the radius of the circle

hope it helps

Answer 3

how do i find h k and r

Answer 4

@campbell_st

Answer 5

so do you know how to complete the square..?

Answer 6

yeah four and -2 work

Answer 7

ok... so in x it becomes

\[(x^2 + 8x + 16) + (y^2 - 4y + 4) = 36 + 16 + 4\]

the values you add to the left, to complete the square need to be added to the right.

so next step is to factor the perfect squares and simplify the right side

what would you get..?

Answer 8

(x+4)(x+4) and (y-2)(y-2)

Answer 9

=56

Answer 10

that's ok... the more correct way to write it is

\[(x + 4)^2 + (y - 2)^2 = 56\]

so if you compare it to the standard form

\[(x -h)^2 + (y - k)^2 = r^2\]

you should be able to identify the centre and radius

Answer 11

thank you

Answer 12

(h, k) is the centre and r is the radius

Answer 13

so (4,-2) and 56