Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0, (a < 0) be 2… and 2…, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to :

Circle

JEE Main 2021 · 16 Mar, Evening shift · Q3083

MathematicsMedium127×since 2002Q3083

Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0, (a < 0) be 2

{\sqrt 2 }

and 2

{\sqrt 5 }

, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to :

JEE Main 2021 · 16 Mar, Evening shift · Q3083

MathematicsMedium127×since 2002Q3083

Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay + c = 0, (a < 0) be 2

{\sqrt 2 }

and 2

{\sqrt 5 }

, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to :