(a)

The equation of shape of a catenary is .

Here length of the wire is arc length of the wire.

The poles are at and .

Consider .

Differentiate with respect to .

Arc length formula : .

Length of the wire is .

Since the minimum legth length of wire occurs at , find .

(b)

The distance between two telephone poles is .

The length of the wire is .

.

Substitute  in the above equation.

.

Draw a coordinate plane.

Graph the function .

Observe the graph, .

Since negative values donot considered then .

Find how high the pole should be attached.

Height function is .

Substitute and in the above expression.

Therefore, wire should be attached from the ground.

(a) The length of the wire is .

(b) The wire should be attached from the ground.