SOLUTION: If y= mx + c is a tangents to the circle x^2 + y^2 =r^2,show that c = rsqrt(1 + m^2}}}. Hence, find the equations of the tangents to the circle x^2 + y^2 = 4 which pass through the

Question 989033: If y= mx + c is a tangents to the circle x^2 + y^2 =r^2,show that c = rsqrt(1 + m^2}}}. Hence, find the equations of the tangents to the circle x^2 + y^2 = 4 which pass through the points (0,+_6).
Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
Centre of is (0,0) and radius r.
Since y=mx+c (or say mx-y+c=0) is tangent to this circle, distance from centre(0,0) to this line is equal to radius
So,

=>
=> --------------part (i)
Let y=mx+c be tangents to circle x^2 + y^2 = 4
Since, it passes through (0,6) and (0,-6)
So,
6=0+c and -6 = 0+c
=> c=6 or -6
Now, using part(i) proof,
or
=> or (from both equations-same values of m)
So equation of tangents are
and and and
Since there are two external points, hence two tangents can be drawn from each point. So, we have got 4 equations of tangents.
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