Find the equation of the circle passing through the origin and the points where the line meets the axes of coordinates.
Explanation for the correct option:
Step:1 Find out the points at which the circle cuts X and Y axis.
The equation of the given line is .
Let, .
Therefore,
Therefore, the point on the Y-axis is .
Let, .
Therefore,
Therefore, the point on the X-axis is .
Therefore, this circle passes through origin and these two points.
Hence, the line that connects these two points is the diameter of the circle.
Step:2 Find out the equation of the circle
Now, the equation of the circle that has a diameter with two points at and is
Therefore, Option(D) is the correct answer.