Final answer:
To find the equation of a straight line that intersects a circle and is at a specific distance from two points, additional information such as the center and radius of the circle is needed to apply geometrical principles and derive the line equation.
Step-by-step explanation:
The question involves finding the equation of a straight line that intersects a circle at two points, which are both 2 units away from a given point on the line. This is a problem that typically involves knowledge of geometry and algebra, both of which are areas of mathematics typically studied at the high school level.
To solve this, we would need more information such as the coordinates of the center of the circle and its radius. With those, we could apply the concept that the perpendicular from the center of the circle to the chord (the straight line) bisects the chord. This is because, from the center of the circle, a radius that is perpendicular to a chord bisects the chord. From this principle, we could derive the equation of the line if the position of those two points on the line (where it intersects the circle) and the radius of the circle were known.
In the case of a circle, the distance from the center to the chord (a line segment inside the circle) is known as the perpendicular from the center to the chord. This bit of geometrical knowledge allows us to set up the necessary equations to find the equation of the line in question.