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If 3x+y=0 is a tangent to a circle whose...

If `3x+y=0` is a tangent to a circle whose center is `(2,-1)` , then find the equation of the other tangent to the circle from the origin.

Text Solution

Verified by Experts

The correct Answer is:
`x-3y=0`
The angle between `3x+y=0` and the line joining (2,-1) to (0,0) is
`theta =tan^(-1)|(-3+(1)/(2))/(1+(-3)(-(1)/(2)))|`
`= tan^(-1)|-1|=(pi)/(4)`
The other tangent is perpendicular to `3x+y=0`
Therefore, the equation of the other tangent is `x-3y=0`.
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