If the chord of contact of the circle $x^{2} + y^{2} - 2 x + 4 y + λ = 0$ with respect to a point lying on the circle $x^{2} + y^{2} - 2 x + 4 y + 1 = 0$ touches the circle $x^{2} + y^{2} - 2 x + 4 y + 3 = 0$ , then the number of value(s) of $λ$ is

Zero

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One

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Two

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Infinitely many

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Solution

The correct option is A Zero
$\to$ AS both the circle have
centers at $(1, - 2) {(- g, - f)}$
$\Rightarrow$ they are concentric circle
$\Rightarrow$ they can't have a chord
of contact touching the
third circle which is also
concentric to the two
$\Rightarrow (A)$

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If the chord of contact of the circle x2+y2−2x+4y+λ=0 with respect to a point lying on the circle x2+y2−2x+4y+1=0 touches the circle x2+y2−2x+4y+3=0, then the number of value(s) of λ is

The correct option is A Zero→ AS both the circle have centers at (1,−2){(−g,−f)}⇒ they are concentric circle ⇒ they can't have a chord of contact touching thethird circle which is also concentric to the two ⇒(A)

If the chord of contact of the circle $x^{2} + y^{2} - 2 x + 4 y + λ = 0$ with respect to a point lying on the circle $x^{2} + y^{2} - 2 x + 4 y + 1 = 0$ touches the circle $x^{2} + y^{2} - 2 x + 4 y + 3 = 0$ , then the number of value(s) of $λ$ is

The correct option is A Zero
$\to$ AS both the circle have
centers at $(1, - 2) {(- g, - f)}$
$\Rightarrow$ they are concentric circle
$\Rightarrow$ they can't have a chord
of contact touching the
third circle which is also
concentric to the two
$\Rightarrow (A)$