A cone of diameter of base 60 mm and height 70 mm is cut by a section plane so that true shape of the section is an ellipse of major axis 50 mm and minor axis 25 mm.  Draw the projections of the cone and find the inclination of cutting plane with H.P.

The inclination of the cutting plane with the horizontal plane (HP) is determined to be approximately 52 degrees based on both graphical and analytical methods. 

### Graphical Method:
1. **Draw the projections of the cone** with a base diameter of 60 mm and height of 70 mm.
2. **Determine the cutting planes** for the minor axis of 25 mm by drawing vertical cutting planes 12.5 mm below and above the center in the top view.
3. **Obtain the curves of intersection** in the front view, which are rectangular hyperbolas.
4. **Draw the actual cutting plane** tangential to the rectangular hyperbola at its midpoint, with a length of 50 mm (major axis) using a trammel or trial and error.
5. **Complete the section and true shape** of the section, confirming an ellipse with major axis 50 mm and minor axis 25 mm.
6. **Measure the inclination** of the cutting plane with the HP, which is approximately 52 degrees.

 

### Analytical Method:
- Using the conditions that the distance between the points where the cutting plane intersects the generators (major axis) is 50 mm and the minor axis is 25 mm, the inclination angle θ is found to satisfy tan θ ≈ 1.315, giving θ ≈ 52.8 degrees, which rounds to 52 degrees for practical purposes.

Thus, the inclination of the cutting plane with the HP is **52 degrees**.

\boxed{52^\circ}