Let the lengths of intercepts on X -axis and y -axis made by the circle x^2+y^2+ ax+2 ay+c=0 (a

Question

Let the lengths of intercepts on X -axis and y -axis made by the circle x^2+y^2+ ax+2 ay+c=0 (a<0 ) be 2 2 and 2 5, respectively. Thenthe shortest distance from origin to a tangent to this circle which is perpendicular to the line x+2y=0, iseuqalto :

Accepted Answer

Correct answer: C. c JEE Main 2021 x^2+y^2+ ax+2 ay+c=0 2 g^2-c=2 a^24-c=2 2 ⇒ a^24-c=2 … . (1 ) 2 f^2-c=2 a^2-c=2 5 ⇒a^2-c=5 (1 ) \& (2 ) 3a^24=3 ⇒a=-2 (a<0 ) ∴c=-1 Circle ⇒x^2+y^2-2x-4y-1=0 ⇒ (x-1 )^2+ (y-2 )^2=6 Given x+2y=0 ⇒m=- 12 m_ tangent=2 Equation of tangent ⇒ (y-2 )=2 (x-1 ) 6 1+4 ⇒2x-y 30=0 Perpendicular distance from (0 ,0 )= ( 30 4+1 )= 6

$Let the lengths of intercepts on X -axis and y -axis made by the circle x^{2} + y^{2} + ax + 2 ay + c = 0 (a < 0) be 22 and 25, respectively. Thenthe shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2 y = 0, iseuqalto :$

Solution

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