Question

The line lx + my + n = 0 will be a tangent to the circle $x^2+y^2=a^2$ iff

• A. $n^2(l^2+m^2)=a^2$
• B. $a^2(l^2+m^2)=n^2$
• C. n(l + m) = a
• D. a(l + m) = n

Answer 1

The correct option is B $a^2(l^2+m^2)=n^2$

Line y = mx + c is tangent, if $c=\pm a\sqrt{1+m^2}.$
Now lx + my + n = 0 or $y=-\frac{1}{m}x-\frac{n}{m}$ is tangent, if $-\frac{n}{m}=\pm a\sqrt{1+{\left(\frac{1}{m}\right)}^2}or{n}^2=a^2(m^2+l^2).$