একটি বৃত্ত (1,-2) বিন্দুগামী এবং X অক্ষকে (3,0) বিন্দুতে স্পর্শ করে তবে উক্ত বৃত্তটি নিচের কোন বিন্দুগামীও হবে?

Since circle touches x-axis at $3, 0$

$\therefore$ The equation of circle be

$(x - 3)^2 + (y - 0)^2 + \lambda y = 0$

A Cartesian coordinate system (x and y axes) with a circle plotted in the fourth quadrant. The x-axis extends horizontally with an arrow pointing right, and the y-axis extends vertically with arrows pointing up and down. The circle touches the x-axis at a point labeled A $3, 0$. Another point, A $1, -2$, is marked on the circumference of the circle in the fourth quadrant.

As it passes through $1, -2$

$\therefore$ Put $x = 1, y = -2$

$(1-3)^2 + (-2)^2 + \lambda(-2) = 0 \Rightarrow \lambda = 4$

$\therefore$ equation of circle is $(x - 3)^2 + y^2 - 8 = 0$

Now, from the options $5, -2$ satisfies equation of

circle.