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

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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