Question

The equations of the tangents drawn from the point $(0,1)$ to the circle $x^2+y^2-2x+4y=0$ are-

• A. $2x-y+1=0,x+2y-2=0$.
• B. $2x-y-1=0,x+2y-2=0$.
• C. $2x-u+1=0,x+2y+2=0$.
• D. $2x-y-1=0,x+2y+2=0$.

Answer 1

The correct option is A $2x-y+1=0,x+2y-2=0$.

Combined equation of tangents drawn from an external point $P(x_1,y_1)$ to the circle $S=0$ are given by $S{S}_{11}=S_1^2$
Eqautions of tangents drawn from $(0,1)$ to $x^2+y^2-2x+4y=0$ are given by $(x^2+y^2-2x+4y)5=(x-3y-2{)}^2$
$\Rightarrow 5x^2+5y^2-10x+20y=x^2+9y^2-6xy-4x+12y+4$
$\Rightarrow 2x^2-2y^2+3xy-3x+4y-2=0$
$\Rightarrow (x+2y-2)(2x-y+1)=0$
$\therefore$ Required tangents are $x+2y-2=0$ and $2x-y+1=0$
Hence, option A.