Question

A line of fixed length a + b, moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is

• A. A parabol
• B. A circle
• C. An ellips
• D. A hyperbol

Hint:

When a line segment divides into parts along fixed lines, the locus of such a point is typically an ellipse due to the constant sum of distances to the two fixed points (foci).

Answer 1

The Correct Option is C

Step 1: A line segment of length \(a + b\) moves with endpoints on two perpendicular lines. A point splits the segment into lengths \(a\) and \(b\). Determine the point's path.

Step 2: This scenario defines an ellipse. An ellipse's points have a constant sum of distances to two foci. Here, the perpendicular lines are axes, and the point's \(a\) and \(b\) division aligns with the ellipse's properties.

Step 3: The point dividing the segment maintains a constant distance relationship to the endpoints, thus tracing an ellipse.