Question

If the equation of the one tangent to the circle with centre at (2, -1) from the origin is 3x + y = 0 then the equation of the other tangent through origin is

• A. $x-3y=0$
• B. $x+3y=0$
• C. $x+2y=0$
• D. $2x+2y=0$

Answer 1

The correct option is A $x-3y=0$

Radius of circle=Length of perpendicular from center of circle an tangent.

$=\frac{13\left(2\right)-11}{\sqrt{10}}=\frac{5}{\sqrt{10}}$

Equation of circle;

${\left(x-2\right)}^2+{\left(y+1\right)}^2=\frac{5}{2}$

Let $y=mx$ be equation of another tangent.

$\begin{array}{c}{\left(x-2\right)}^2+{\left(mx+1\right)}^2=\frac{5}{2}\\ \left(1+m^2\right)x^2+4-4x+1+2mx=\frac{5}{2}\\ \left(1+m^2\right)x^2+\left(2m-4\right)x=\frac{5}{2}\\ {\left(2m-4\right)}^2-4\left(1+m^2\right)\frac{5}{2}=0\\ 3m^2+8m-3=0\\ 3m^2+9m-m-3=0\\ \left(3m-1\right)\left(m+3\right)=0\\ m=\frac{1}{3},-3\\ equationofother\tan genty=\frac{x}{3}\\ x-3y=0\end{array}$

Hence, this is the answer.