On which of the following projection the equator can not be shown?

Question

Accepted Answer

The correct answer is Option 4: Gnomonic Polar Zenithal Projection. Here's why:

*   **Gnomonic Polar Zenithal Projection and the Equator:** Gnomonic projections project points from the center of the globe onto a tangent plane. In a *polar* gnomonic projection, the plane is tangent to the globe at one of the poles (North or South). Because the equator is 90 degrees away from the pole, projecting the equator from the center of the Earth onto the tangent plane would require lines that are parallel to the plane. Parallel lines, by definition, never intersect. Therefore, the equator cannot be represented on a gnomonic polar zenithal projection; it would project to infinity.

Now, let's explain why the other options are incorrect:

*   **Option 1: Polyconic Projection:** Polyconic projections use a series of cones tangent to the globe at different latitudes. The equator *can* be shown on a polyconic projection, although it may not be perfectly represented in terms of shape or scale. It's a standard line on the projection.

*   **Option 2: Bonne's Projection:** Bonne's projection is a pseudoconic equal-area projection. It uses a standard parallel, and all other parallels are projected as arcs of circles centered on the axis. The equator *can* be represented on Bonne's projection, although distortion increases away from the standard parallel.

*   **Option 3: Stereographic Polar Zenithal Projection:** Stereographic projections project points from a point on the globe's surface (opposite the tangent point) onto a tangent plane. In a polar stereographic projection, the plane is tangent at the pole. The equator *can* be shown on a stereographic polar zenithal projection. It appears as a circle centered on the pole. While there is distortion, the equator is still representable.

Therefore, only the Gnomonic Polar Zenithal Projection (Option 4) cannot represent the equator because it would project to infinity.