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Q.
The equation of the chord of contact of the tangents drawn from $(1,2)$ to the circle $x^{2}+y^{2}-2 x+4 y+7=$ 0, is (are)
Conic Sections
Solution:
Given circle is $x^{2}+y^{2}-2 x+4 y+7=0$.....(i)
Let $P=(1,2)$
For point $P (1,2)$,
$x^{2}+y^{2}-2 x+4 y+7=1+4-2+8+7=18>0$
Hence point P lies outside the circle
For point $P (1,2), T = x .1+ y \cdot 2-( x +1)+2( y +2)+7$
i.e., $T=4 y+10$
Now equation of the chord of contact of point $P(1,2)$ w. r. t. circle
(i) will be
$4 y+10=0 $ or $2 y+5=0$