Question

Find the equation of the tangent lines to the circle $x^2+y^2=9$ which are parallel to the line $2x+y-3=0$.

Answer 1

Equation of circle is $x^2+y^2=9$

equation of tangent parallel to $2x+y-3=0$ is $2x+y+\lambda =0$

its distance from centre $=$ radius of the circle.

radius of circle $=3$ units.

$\therefore$ $\frac{|2\times 0+0+\lambda |}{\sqrt{4+1}}=3$

$\Rightarrow \lambda =3\sqrt{5}$

$\therefore$ Equation of tangent is $2x+y+3\sqrt{5}=0$