When the plane cuts the nappe( other than the vertex) of the cone, we have the following situations:
( a) When β = 90 o, the section is a circle.( b) When α < β < 90 o, the section is an ellipse.( c) When β = α; the section is a parabola.
( d) When 0 ≤ β < α; the plane cuts through both the nappes & the curves of intersection is a hyperbola
Let’ s study each of this conic section in details. Circle
A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.
The fixed point is called the centre of the circle and the distance from the centre to a point on the circle is called the radius of the circle
Numerical: Find the equation of the circle with centre(– 3, 2) and radius 4.
Solution Here h = – 3, k = 2 and r = 4. Therefore, the equation of the required circle is
( x + 3) 2 +( y – 2) 2 = 16