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Question

A circle passing through the points A(1,0) and B(5,0) and touches the Y-axis at C(0,λ). If ACB is maximum, then?

A
|λ|=5
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B
|λ|=25
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C
|λ|=35
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D
|λ|=45
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Solution

The correct option is A |λ|=5
Eq. of AC=0λ=m(10)m=λ
Eq. of BC=0λ=m(50)m=λ5

Slope of Line AC tanθ=λ1
Slope of Line BC tanθ1=λ5
ACB=π+tan1λ1πtan1λ5
ACB=tan1λ5+tan1λ1
dACBdλ=5λ2+25+1λ2+1

Equating to zero, we get -
5λ2+5=λ2+25
4λ2=20
|λ|=5

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