Question

Write the equation of the circle centered at (6, 2) with radius 1. Fully simplify the equation.

Answer 1

`x^2-12x+y^2-4y+39=0`

Explanation:

`\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}`

Given:

• center = (6, 2)
• radius = 1

Substitute the given values into the equation of a circle formula:

`\implies (x-6)^2+(y-2)^2=1^2`

Simplify by expanding:

`\implies (x-6)(x-6)+(y-2)(y-2)=1`

`\implies x^2-12x+36+y^2-4y+4=1`

`\implies x^2-12x+y^2-4y+39=0`