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 $x^{2}+y^{2}-6 x-4 y+9=0$
$C=(3,2), r=2$
If line $4 x+3 y-8=0$ 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.