Question

The equations of the circles which touch the y-axis at the origin and the line 5x + 12y – 72 = 0 is

• A. + - 6y = 0, + + 24y = 0
• B. + + 2y = 0, + - 18y = 0
• C. + + 18x = 0, + - 8x = 0
• D. + + 4x = 0, + - 16x = 0

Answer 1

The correct option is C + + 18x = 0, + - 8x = 0

Circles touches y-axis at the origin $\Rightarrow$ centre (r, 0), radius = $\left|r\right|$
Circles touches 5x + 12y - 72 = 0 $\Rightarrow$ $\frac{|5r-72|}{13}$ = $\left|r\right|$ $\Rightarrow$ 5r - 72 = $\pm$ 13r $\Rightarrow$ 5r $\mp$ 13r = 72 $\Rightarrow$ r = 4; - 9
$\therefore$ Circle equation are $(x-4{)}^2$ + $y^2$ = $4^2$, or $(x+9{)}^2$ + $y^2$ = $4^2$ $\Rightarrow$ $x^2$ + $y^2$ - 8x = 0, $x^2$ + $y^2$ + 18x = 0