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## Homework Statement

If the equation of one tangent to the circle with center at (2, -1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is:

(a) 3x - y = 0

(b) x + 3y = 0

(c) x - 3y = 0

(d) x + 2y = 0

## Homework Equations

An equation of the tangent to the circle [tex]x^2 +y^2 + 2gx + 2fy + c = 0[/tex] at the point [tex]( x_{1}, y_{1})[/tex] on the circle is

xx

_{1}+ yy

_{1}+ g(x + x

_{1}) + f (y + y

_{1}) + c = 0

There are more but I presume that you know

## The Attempt at a Solution

I've already solved this question from another method but just asking out of my curiosity.

I've learned it on my lower classes that radius are perpendicular to the tangent of the circle. It means that we must get m

_{1}. m

_{2}= -1 but as you can see we are not getting, neither in the case of first tangent nor in the case of second (in any of the option given). Can you tell me, why?