Question

If the points $(2,0),(0,1),(4,5)$ and $(0,c)$ are concydic, then the value of $c$ is

• A. $1$
• B. $\frac{14}{3}$
• C. $5$
• D. None of these

Answer 1

Answer: (B)

The equation of the circle passing through $(2,0),(0,1)and(4,5)$ is
$3\left(x^2+y^2\right)-13x-17y+14=0$
This passes through $(0,c)$.
$\therefore 3c^2-17c+14=0$
$\Rightarrow c=1,\frac{14}{3}$
Since, $c=1$ is already there, for point (0,1)
Therefore, we take $c=\frac{14}{3}$.