Question

$x^2+y^2+6x+8y-11=0$ ( chord of contact)

Answer 1

For $x^2+y^2+2gx+2fx+c=0$
Chord of contact from $(x_1,y_1)$ is
$x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+c=0$
So, for $x^2+y^2+6x+8y-11=0$
Chord of contact from $(x_1,y_1)$ is
$x{x}_1+y{y}_1+3(x+x_1)+4(y+y_1)-11=0$
1) For $(1,1)$, equation is
$x.1+y.1+3(x+1)+4(y+1)-11=0\Rightarrow 4x+5y-4=0$
2) For $(0,0)$, equation is
$x.0+y.0+3(x+0)+4(y+0)-11=0\Rightarrow 3x+4y-11=0$
3) For $(1,-1)$, equation is
$x.1+y.-1+3(x+1)+4(y-1)-11=0\Rightarrow 4x+3y-12=0$
4) For $(-1,-1)$, equation is
$x.-1+y.-1+3(x-1)+4(y-1)-11=0\Rightarrow 2x+3y-18=0$