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**1. Homework Statement**

Find the equation of the tangent of the circular [itex]K:x^2 + y^2 - 2x + 4y=0[/itex], perpendicular to the line x-2y+9=0.

**2. Homework Equations**

[itex](x_1-p)(x-p)+(y_1-q)(y-q)=r^2[/itex], equation of K.

[itex](kp-q+n)^2=r^2(k^2+1)[/itex], condition for tangent and circular K

**3. The Attempt at a Solution**

I tried like this. From the equation [itex]K:x^2 + y^2 - 2x + 4y=0[/itex],

p=1 and q=-2 ,[itex]r^2=5[/itex]

also from x-2y+9=0, the coefficient k of the equation of the tangent should be k=-2.

So I have y=-2x+n, and -2x-y+n=0

[itex](-2*1+2+n)^2=5(4+1)[/itex]

from here I get [itex]n_1=-5[/itex], and [itex]n_2=5[/itex], so the equation should be:

y=-2x-5

y=-2x+5

But the problem is that it is not same with my text book results. Any help?