Question

write the general conic form equation of the circle
(x-4)^2+(y+8)^2=4
with steps please

Answer 1

General equation of circle

• (x-h)²+(y-k)^2=r^2

• Circle has centre (h,k) and radius r

So

here rearrange

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

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

• Centre =(4,-8)
• Radius=2units

Answer 2

Answer:

$x^2+y^2-8x+16y+76=0$

Step-by-step explanation:

General conic form equation of a circle:   $x^2+y^2+ax+by+c=0$

Given equation:

$(x-4)^2+(y+8)^2=4$

Rewrite:

$(x-4)(x-4)+(y+8)(y+8)=4$

Expand brackets:

$x^2-4x-4x+16+y^2+8y+8y+64=4$

Collect and combine like terms:

$x^2-8x+y^2+16y+80=4$

Subtract 4 from both sides:

$x^2-8x+y^2+16y+76=0$

Rearrange:

$x^2+y^2-8x+16y+76=0$