Question

With origin as a focus and x = 4 as the corresponding directrix, a family of ellipses are drawn. Then the locus of an end of the minor axis is:

• A. A circle
• B. A parabola
• C. A straight line
• D. A hyperbola

Hint:

The locus of a point on the minor axis of an ellipse, when defined by a focus and a directrix, forms a parabola.

Answer 1

The Correct Option is B

Step 1: The problem concerns ellipses, with the origin as a focus and \(x = 4\) as the directrix. A key characteristic of ellipses is that the sum of the distances from any point on the ellipse to the two foci remains constant.

Step 2: Considering the minor axis of the ellipse, the endpoint's path resembles a parabola. This stems from the focus and directrix definition of a parabola, a fundamental aspect of conic sections. The directrix is a line, and the focus is fixed at the origin.

Step 3: Consequently, under these constraints, the endpoint of the minor axis traces a parabola.