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

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

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`