Question

A certain circle can be represented by the following equation. x^2+y^2+16x-14y+49=0x 2 +y 2 +16x−14y+49=0x, squared, plus, y, squared, plus, 16, x, minus, 14, y, plus, 49, equals, 0 What is the center of this circle ? ((left parenthesis ,,comma ))right parenthesis What is the radius of this circle ? units

Answer 1

The circle is centered at (8,0)

The circle has a radius of 10 units.

Explanation:

trust

Answer 2

center = (-8, 7)

radius = 8 units

Explanation:

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

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

Rewrite the given equation:

`x^2+y^2+16x-14y+49=0`

`\implies x^2+16x+y^2-14y+49=0`

`\implies (x+8)^2-64+(y-7)^2-49+49=0`

`\implies (x+8)^2+(y-7)^2=64`

Therefore:

• center = (-8, 7)
• radius:
  `r^2=64 \implies r=√(64) =8`