Question

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

A
Zero
B
One
C
Two
D
Infinitely many

Solution

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

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