Question

The equation of the circle having centre at (3, – 4) and touching the line 5x + 12y – 12 = 0 is ______.

Answer 1

The equation of the circle having centre at (3, – 4) and touching the line 5x + 12y – 12 = 0 is `(x - 3)^2 + (y + 4)^2 = (45/13)^2`.

Explanation:

Given equation of the line is 5x + 12y – 12 = 0 and the centre is (3, – 4)

CP = radius of the circle

`|(5 xx 3 + 12 xx (-4) - 12)/sqrt((5)^2 + (12)^2)|` = r

⇒ `|(15 - 48 - 12)/13|` = r

⇒ `|(-45)/13|` = r

⇒ `r^2 = 2025/169`

So, the equation of the circle is  `(x - 3)^2 + (y + 4)^2 = (45/13)^2`