Question

The position of line $3x+4y-6=0$ with respect to the circle $x^2+y^2+2x+8y+1=0$ is

• A. Chord
• B. Tangent
• C. lies outside the the circle
• D. Diameter

Answer 1

The correct option is C lies outside the the circle

Given equation of circle,
$x^2+y^2+2x+8y+1=0$
$C\equiv (-1,-4)r=\sqrt{(-1{)}^2+(-4{)}^2-1}=4$
Perpendicular distance from center to line $3x+4y-6=0$ is $p=\frac{|3\times -1+4\times -4-6|}{\sqrt{(3^2+4^2)}}=5\Rightarrow p>r$

Hence, line $3x+4y-6=0$ lies outside the circle.