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Question

For what value of λ, the line 4x+3y+λ=0 will be tangent to the circle x2+y26x+4y12=0 ?

A
19
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B
19
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C
31
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D
31
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Solution

The correct options are
A 19
C 31
Centre and the radius of the circle are (3,2) and 9+4+12=5
Thus for given line to be tangent to the circle, the distance of line from centre of the
circle should be equal to it's radius.
∣ ∣4(3)+3(2)+λ32+42∣ ∣=5
6+λ=±25λ=19,31

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