<\/span><\/h4>\nA circle is the set of all points in a plane, which are at a fixed distance from a fixed point in the plane. The fixed point is called the centre of the circle and the distance from centre to any point on the circle is called the radius of the circle.
The equation of a circle with radius r having centre (h, k) is given by (x \u2013 h)2<\/sup>\u00a0+ (y \u2013 k)2<\/sup>\u00a0= r2<\/sup>.<\/p>\nThe general equation of the circle is given by x2<\/sup>\u00a0+ y2<\/sup>\u00a0+ 2gx + 2fy + c = 0 , where, g, f and c are constants.<\/p>\n\n- The centre of the circle is (-g, -f).<\/li>\n<\/ul>\n
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The general equation of the circle passing through origin is x2<\/sup>\u00a0+ y2<\/sup>\u00a0+ 2gx + 2fy = 0.<\/p>\nThe parametric equation of the circle x2<\/sup>\u00a0+ y2<\/sup>\u00a0= r2<\/sup>\u00a0are given by x = r cos \u03b8, y = r sin \u03b8, where \u03b8 is the parametre and the parametric equation of the circle (x \u2013 h)2<\/sup>\u00a0+ (y \u2013 k)2<\/sup>\u00a0= r2<\/sup>\u00a0are given by x = h + r cos \u03b8, y = k + r sin \u03b8.<\/p>\nNote: The general equation of the circle involves three constants which implies that at least three conditions are required to determine a circle uniquely.<\/p>\n
Parabola<\/p>\n
In a parabola, the set of points P have distances from a fixed point F in one plane and equal in distance from a fixed line I in the place. F is called the focus and the fixed line I is called directrix of the parabola.<\/p>\n
\n\n\n| \n Forms of parabola<\/p>\n<\/td>\n | \n y2= 4ax<\/p>\n<\/td>\n | \n y2 = -4ax<\/p>\n<\/td>\n | \n x2 = 4ay<\/p>\n<\/td>\n | \n x2 = -4ay<\/p>\n<\/td>\n<\/tr>\n |
\n| \n Axis of parabola<\/p>\n<\/td>\n | \n y = 0<\/p>\n<\/td>\n | \n y = 0<\/p>\n<\/td>\n | \n x = 0<\/p>\n<\/td>\n | \n x = 0<\/p>\n<\/td>\n<\/tr>\n |
\n| \n Directrix of parabola<\/p>\n<\/td>\n | \n x = -a<\/p>\n<\/td>\n | \n x = a<\/p>\n<\/td>\n | \n y = -a<\/p>\n<\/td>\n | \n y = a<\/p>\n<\/td>\n<\/tr>\n |
\n| \n Vertex<\/p>\n<\/td>\n | \n (0, 0)<\/p>\n<\/td>\n | \n (0, 0)<\/p>\n<\/td>\n | \n (0, 0)<\/p>\n<\/td>\n | \n (0, 0)<\/p>\n<\/td>\n<\/tr>\n |
\n| \n Focus<\/p>\n<\/td>\n | \n (a, 0)<\/p>\n<\/td>\n | \n (-a, 0)<\/p>\n<\/td>\n | \n (0, a)<\/p>\n<\/td>\n | \n (0, -a)<\/p>\n<\/td>\n<\/tr>\n |
\n| \n Length of latus rectum<\/p>\n<\/td>\n | \n 4a<\/p>\n<\/td>\n | \n 4a<\/p>\n<\/td>\n | \n 4a<\/p>\n<\/td>\n | \n 4a<\/p>\n<\/td>\n<\/tr>\n |
\n| \n Focal length<\/p>\n<\/td>\n | \n |x + a|<\/p>\n<\/td>\n | \n |x \u2013 a|<\/p>\n<\/td>\n | \n |y + a|<\/p>\n<\/td>\n | \n |y \u2013 a|<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n |
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