Question

Write the equation of a circle whose center is at (-11,15) and whose radius is 9

Your answer must be in Standard Form AND simplified

Answer 1

`\textsf{Standard form}: \quad (x+11)^2+(y-15)^2=81`

`\textsf{Simplified form}: \quad x^2+22x+y^2-30y+265=0`

Explanation:

`\boxed{\begin{minipage}{6 cm}\underline{Equation of a circle in standard form}\\\\$(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 the center is (-11, 15) and the radius is 9:

• a = -11
• b = 15
• r = 9

Substitute the values of a, b and r into the equation of a circle:

`\implies (x-(-11))^2+(y-15)^2=9^2`

`\implies (x+11)^2+(y-15)^2=81`

To write the equation in simplified form, expand the brackets:

`\implies x^2+22x+121+y^2-30y+225=81`

Collect like terms:

`\implies x^2+22x+y^2-30y+225+121-81=0`

`\implies x^2+22x+y^2-30y+265=0`