Question

Let the equation of circle is $x^2+y^2-6x-4y+9=0$ . Then the line $4x+3y-8=0$ is a

• A. tangent of the circle
• B. normal of the circle
• C. chord of the circle
• D. None of the above

Answer 1

Answer: (A)

Given circle is $x^2+y^2-6x-4y+9=0$
$C=(3,2),r=2$
If line $4x+3y-8=0$ is a tangent to the circle, then
$\left|\frac{4(3)+3(2)-8}{\sqrt{16+9}}\right|=2$
$\Rightarrow \left|\frac{10}{5}\right|=2\Rightarrow 2=2$
Hence, it is a tangent of the circle.