What figure can be obtained by cutting a cone with a plane parallel to the contour line of the cone? Is it a parabola?

What figure can be obtained by cutting a cone with a plane parallel to the contour line of the cone? Is it a parabola?

It depends on where it comes from
Through the vertex, it is an isosceles triangle
Outside the vertex is a parabola like plane
Over the outermost end, there is a point