Question

Find the equation of the circle with `(1/2, 1/4)`and radius `1/12`

Answer 1

The equation of a circle with centre (h, k) and radius r is given as

(x­ – h)² + (y ­– k)² = r²

It is given that centre (h, k) = `(1/2, 1/4)` and radius (r) = `1/12`

Therefore, the equation of the circle is

`(x - 1/2)^2 + (y - 1/4)^2 = (1/12)^2`

`x^2 - x + 1/4 + y^2 - y/2 + 1/16 = 1/144`

`x^2 - x + 1/4 + y^2 - y/2 + 1/16 - 1/144 = 0`

144x² - 144x + 36 + 144y − 72y + 9 - 1 = 0

144x² - 144x + 144y² − 72y + 44 = 0

36x² - 36x + 36y² − 18y + 11 = 0

36x² + 36x² − 36x − 18y + 11 = 0