Question

The equation of a circle is $x^2+y^2-4x+2y-4=0$. With respect to the circle

• A. the pole of the line $x-2y+5=0$ is $(1,1)$
• B. the chord of contact of real tangents from $(1,1)$ is the line $x-2y+5=0$
• C. the polar of the point $(1,1)$ is $x-2y+5=0$
• D. none of these

Answer 1

Answer: (A), (B), (C)

the pole of the line $x-2y+5=0$ is $(1,1)$
the chord of contact of real tangents from $(1,1)$ is the line $x-2y+5=0$
the polar of the point $(1,1)$ is $x-2y+5=0$

let $(1,1)$ be pole of $x^2+y^2-4x+2y-4=0$

Then equation of polar which is also chord of contact is $S_1=0$

$1.x+1.y-2(x+1)+y+1-4=0$

$x-2y+5=0$
Ans: A,B,C