Question

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.
x2 − 4x + y2 + 8y = −4

Answer 1

$\\ \rm\rightarrowtail x^2-4x+y^2+8y=-4$

$\\ \rm\rightarrowtail x^2-2(x)(2)+y^2+2(4)(x)=-4$

• Add 4 and 16

$\\ \rm\rightarrowtail x^2-2(2x)+4+y^2+2(4x)+16=-4+4+16$

$\\ \rm\rightarrowtail x^2-2(2x)+2^2+y^2+2(4x)+4^2=16$

$\\ \rm\rightarrowtail (x-2)^2+(y+4)^2=4^2$

• (x-h)^2+(y-k)^2=r^2

so

• Centre(h,k)=(2,-4)
• radius=4

Answer 2

Answer:

center = (2, -4)

radius = 4

Step-by-step explanation:

$\sf x^2-4x+y^2+8y=-4$

$\sf \implies x^2-4x+4+y^2+8y+16=-4+4+16$

$\sf \implies (x-2)^2+(y+4)^2=16$

Equation of a circle: $\sf (x-h)^2+(y-k)^2=r^2$

(where (h, k) is the center and r is the radius)

Therefore,

• center = (2, -4)
• radius = √16 = 4