Question

The equation of the chord of contact of the tangents drawn from $(1,2)$ to the circle $x^2+y^2-2x+4y+7=$ 0, is (are)

• A. $4y+10=0$ or $2y+5=0$
• B. $4y-10=0$ or $2y+5=0$
• C. $4y+10=0$ or $2y-5=0$
• D. None

Answer 1

Answer: (A)

Given circle is $x^2+y^2-2x+4y+7=0$.....(i)
Let $P=(1,2)$
For point $P(1,2)$,
$x^2+y^2-2x+4y+7=1+4-2+8+7=18>0$
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., $T=4y+10$
Now equation of the chord of contact of point $P(1,2)$ w. r. t. circle
(i) will be
$4y+10=0$ or $2y+5=0$