Question

Write the equation of the circle centered at (-6, - 10) with radius 18.

Answer 1

`(x+6)^2 +(y+10)^2 = 324`

Explanation:

`\underline{\textbf{Equation of circle(Standard form)}}\\\\~~~~~~~~~~~~~~~~~~~~(x-h)^2 + (y-k)^2 =r^2\\\\\text{Where,}\\\\(h,k) = \text{Center of the circle.}\\\\r = \text{Radius of the circle.}\\`

`\underline{\textbf{Solution:}}\\\\\text{Given that,}\\\\\text{Center of the circle,}~ (h,k) = (-6,-10)\\\\\text{Radius of the circle,}~ r = 18~ \text{units.}\\\\\text{From the given data, the equation of the circle is,}\\\\~~~~~~~~~~~~~~~~~~~~(x-h)^2 +(y-k)^2 = r^2\\\\~~~~~~~~~~~\implies (x-(-6))^2+ (y-(-10))^2 = 18^2\\\\~~~~~~~~~~~\implies \boxed{(x+6)^2 +(y+10)^2 = 324}`

Answer 2

(x + 6)² + (y + 10)² = 324

Explanation:

Formula:

The equation of a circle centered at (a , b) with radius r is :

(x − a)² + (y − b)² = r²

……………………………………

then

the equation of the circle centered at (-6, - 10) with radius 18 is :

(x − (-6))² + (y − (-10))² = 18²

⇔ (x + 6)² + (y + 10)² = 324

⇔ x² + 12x + y² + 20y - 188 = 0