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 .