(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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?

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# Homework Help: Equation for the tangent of a circle

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