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Question

If α is the angle subtended at P(x1,y1) by the circle S=x2+y2+2gx+2fy+c=0, then

A
cotα=S1g2+f2c
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B
cotα/2=S1g2+f2c
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C
tanα=2g2+f2cS1
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D
α=2tan1(g2+f2cS1)
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Solution

The correct options are
C cotα/2=S1g2+f2c
D α=2tan1(g2+f2cS1)
where S1=x21+y21+2gx1+2fy1+c Ans. (b) and (d)
Solution Let PA and PB he the tangents from P(x1,y1) to the given circle with centre C(gf), such that APB=θ. Then APC=θ/2(Fig.16.31). Therefore, from Δ.PAC, we get
cot=θ2=PAAC=S1g2+f2c
tan=θ2=g2+f2cS1
θ=2tan1(g2+f2cS1)
243537_196677_ans_8fe8753fc82c4c049f86bd4138ff83de.png

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