Equation of Conic Section ( a , b , g , f , h , c are constants ) :
ax² + by² + 2gx + 2fy + 2hxy + c = 0
x² +
y² +
x +
y +
xy +
= 0 This is
This is
This is
Use the formulae- delta = abc + 2fgh - af² -bg² - ch² if delta = 0 ....... it is a pair of straight lines . If delta =0 & h²=ab..pair of || st. lines if delta not equal to zero for a = b and h = 0 .......... circle h² = ab ........... parabola h² < ab ........... ellipse h² > ab ........... hyperbola h² > ab and a + b = 0 ...........rectangular hyperbola if of the form ax² + by² + 2hxy = 1 ....It is a central conic( inclined ellipse if h*h < ab) . Angle of inclination is tan 2M =2tanM/(1 - tan²M) = 2h /(a - b ) Angle M will lie between - 45 degree to + 45 degree . It will have 2 values M1 , M2 . M1 + M2 = 90