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Q.

If 3x+y=0 tangent to the circle having its centre at (2, -1), then the equation of other tangent to the circle from the origin, is

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a

x−3y=0

b

x+3y=0

c

3x−y=0

d

2x+y=0

answer is A.

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Detailed Solution

Let y = mx be a tangent drawn from the origin to the circle having its centre at (2, -1) and touching 3x+y=0Then,2m+1m2+1=6−19+1⇒2(2m+1)2=5m2+1⇒3m2+8m−3=0⇒(3m−1)(m+3)=0⇒m=−3,13Thus, the equation of the tangents drawn from the origin arey=−3x and y=x/3
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If 3x+y=0 tangent to the circle having its centre at (2, -1), then the equation of other tangent to the circle from the origin, is