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