Question

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle

• A. $4x-3y+17=0$
• B. $3x+4y-6=0$
• C. $4x+3y-8=0$
• D. $3x-4y-24=0$

Answer 1

Answer: (C)

Equation of family of circle touching y-axis at $\left(0,4\right)$ is given by ${\left(x-0\right)}^2+{\left(y-4\right)}^2+\lambda x=0.$
$\because$ It passes through $\left(2,0\right)$
$\Rightarrow \lambda =-10$
$\Rightarrow$ Required circle is ${\left(x-0\right)}^2+{\left(y-4\right)}^2-10x=0$
$\Rightarrow x^2+y^2-10x-8y+16=0$
center of circle $\equiv \left(5,4\right)$ and radius $=5$ distance of $4x+3y-8=0$ from $\left(5,4\right)$
$=\left|\frac{24}{5}\right|\ne$ radius