In the equation ax2-2hxy-by2-2gx-2fy-c-0- if a-b-h-1 and f- g- then eccentricity of the conic is

Clearly, h^2=ab =abc+2fgh af^2 bg^2 ch^2 =c+2fg f^2 g^2 c = (f g)^2 Since f≠ g, we have ≠0 ∴ The conic is parabola ⇒ e=1 ...

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Distinguishing between Conics from General Equation and Eccentricity

In the equati...

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In the equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0,$ if $a = b = h = 1$ and $f \neq g,$ then eccentricity of the conic is

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a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0,

a = b = h = 1

f \neq g,

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

h^{2} > a b

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

h^{2} < a b

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

h^{2} = a b

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

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