Previous Year NEET Question- Circles

2016:

The equation of a circle with center $(h, k)$ and radius $r$ is given by:

$$ (x - h)^2 + (y - k)^2 = r^2 $$

We are given that the circle passes through the origin, so $(h, k) = (0, 0)$. We are also given that the circle has intercepts $4$ and $3$ on the $x$-axis and $y$-axis, respectively. This means that the circle must pass through the points $(4, 0)$ and $(0, 3)$. The equation of the line $x = 4$ is not $y = 0$, and the equation of the line $y = 3$ is not $x = 0$. So, the circle must pass through the points $(0, 0)$, $(4, 0)$, and $(0, 3)$.

We can find the equation of the circle by using the following steps:

1. Find the center of the circle by averaging the coordinates of the points that it touches.
2. Find the radius of the circle by using the distance formula to find the distance from the center to any point on the circle