What is the difference between ellipse, parabola, and hyperbola in conic sections?

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What is the difference between ellipse, parabola, and hyperbola in conic sections?

Sumit Saini 21st Jul, 2020

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Sumit Saini 21st Jul, 2020

Features	Ellipse	Parabola	Hyperbola
Definition	A set of points where the sum of the distances from two fixed foci is constant.	A set of points equidistant from a fixed point called the focus and a fixed line called the directrix.	A set of points where the absolute difference of distances from two fixed foci is constant.
Shape	Oval shaped	U-shaped	Two separate open curves(Look like two infinite bows)
Standard Equation	$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$	$y^2=4 a x$	$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
Foci	$( \pm c, 0) \text {, where } c^2=a^2-b^2$	$(a, 0)$	$( \pm c, 0) \text {, where } c^2=a^2+b^2$
Eccentricity (e)	$0<e<1$	$e=1$	$e>1$

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