If the tangents are drawn from any point on the line $ x+y=3 $ to the circle $ x^{2}+y^{2}=9 $, then the chord of contact always passes through a fixed point. Find that point

Question

If the tangents are drawn from any point on the line $ x+y=3 $ to the circle $ x^{2}+y^{2}=9 $, then the chord of contact always passes through a fixed point. Find that point, $ (3,5) $, $ (3,3) $, $ (5,3) $, none of these

MARKS App · Accepted Answer

Let α , 3 - α be any point on x + y = 3 ∴ Equation of chord of contact is α x + 3 - α y = 9 i.e. α x - y + 3 y - 9 = 0 The chord passes through the point 3 , 3 for all values of α .

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