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 involves ellipses with the origin as the focus and \(x = 4\) as the directrix. For ellipses, the general property is that the sum of distances from any point on the ellipse to the two foci is constant.

Step 2: When we focus on the minor axis of an ellipse, the locus of the end of the minor axis behaves like a parabola. This is because the directrix and the focus define a parabolic shape, a known property of conic sections. The directrix acts as a line, and the focus remains fixed at the origin.

Step 3: Therefore, the locus of the end of the minor axis, given these conditions, forms a parabola.