Question

The equation of a circle touching the axes of coordinates and the line $x \cos \alpha + y \sin \alpha = 2$can be.

• A. $x ^ { 2 } + y ^ { 2 } - 2 g x - 2 g y + g ^ { 2 } = 0$ , where $g = \frac { 2 } { ( \cos \alpha + \sin \alpha + 1 ) }$
• B. $x ^ { 2 } + y ^ { 2 } - 2 g x - 2 g y + g ^ { 2 } = 0$ , Where $g = \frac { 2 } { ( \cos \alpha + \sin \alpha - 1 ) }$
• C. $x ^ { 2 } + y ^ { 2 } - 2 g x + 2 g y + g ^ { 2 } = 0$, Where $g = \frac { 2 } { ( \cos \alpha - \sin \alpha + 1 ) }$
• D. $x ^ { 2 } + y ^ { 2 } - 2 g x + 2 g y + g ^ { 2 } = 0$ Where $g = \frac { 2 } { ( \cos \alpha - \sin \alpha - 1 ) }$ (5) All of these

Answer 1

(5)

Sol. $x ^ { 2 } + y ^ { 2 } - 2 g x - 2 g y + g ^ { 2 } = 0$

$g = \pm \frac { g \cos \alpha + g \sin \alpha - 2 } { \sqrt { \sin ^ { 2 } \alpha + \cos ^ { 2 } \alpha } }$ ⇒ $g = \frac { 2 } { \sin \alpha + \cos \alpha \pm 1 }$.

Similarly other options hold.