Numerical: Find the centre and the radius of the circle x 2 + y 2 + 8x + 10y – 8 = 0
Solution The given equation is( x 2 + 8x) +( y 2 + 10y) = 8 Completing the squares, we get( x 2 + 8x + 16) +( y 2 + 10y + 25) = 8 + 16 + 25 i. e.( x + 4) 2 +( y + 5) 2 = 49 = 7 2 Therefore, the given circle has centre at(– 4, – 5) and radius 7. Parabola
A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point( not on the line) in the plane.
Fixed line is called directrix of parabola Fxed point F is called the focus. A line through focus & perpendicular to directrix is called axis. Point of intersection of parabola with axis is called vertex.