Question

Find the equation of the tangents to the circle $x^2+y^2=9$ which
are parallel to the line $3x+4y=2$

Answer 1

$y=mx+c$ is tangent to a circle $x^2+y^2=9$

if $c^2=9(m^2+1)$

Given tangent is parallel to $y=\frac{-3x}{4}+\frac{1}{2}$

$\Rightarrow m=\frac{-3}{4}$

$\therefore c^2=9(\frac{9}{16}+1)$

$=\frac{9\times 25}{16}$

$c=\pm \frac{3\times 5}{4}$

$=\pm \frac{15}{4}$

$\therefore$ Tangents required :

$y=\frac{-3x}{4}\pm \frac{15}{4}$

$\Rightarrow 4y+3x=\pm 15$