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Conics-Formula Sheet

The document provides a comprehensive overview of the equations and properties of conic sections, including parabolas, ellipses, and hyperbolas. It details their respective equations, foci, axes of symmetry, vertices, directrix, lengths of major and minor axes, and relationships between parameters. Each conic section is categorized based on its orientation and characteristics, with specific formulas and definitions included.

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shaurya.rathour1180
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179 views1 page

Conics-Formula Sheet

The document provides a comprehensive overview of the equations and properties of conic sections, including parabolas, ellipses, and hyperbolas. It details their respective equations, foci, axes of symmetry, vertices, directrix, lengths of major and minor axes, and relationships between parameters. Each conic section is categorized based on its orientation and characteristics, with specific formulas and definitions included.

Uploaded by

shaurya.rathour1180
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Formulae of Conics at a glance

Conic Equation and Focus Axis of Vertex/ Equation Length of Length of Length of Relationship
Type /Foci Symmetry Vertices of Major Axis Minor Axis Latus between a,b and c
Directrix /Tranverse /Conjugate Rectum
Axis Axis
Parabola 𝑦 2 = 4𝑎𝑥 (a,0) x-Axis (0,0) x= -a NA NA 4a NA
Opening
Rightwards
a>0 𝑦 2 = −4𝑎𝑥 (-a,0) x-Axis (0,0) x= a NA NA 4a NA
e=c/a Opening
=1 leftwards

𝑥 2 = 4𝑎𝑦 (0,a) y-Axis (0,0) y=-a NA NA 4a NA


Opening
Upwards
𝑥 2 = −4𝑎𝑦 (0,-a) y-Axis (0,0) y= a NA NA 4a NA
Opening
Downwards
Ellipse 𝑥2 𝑦2 (±𝑐, 0) x-Axis (±𝑎, 0) NA 2a 2b 2𝑏2 𝑐 2 = 𝑎2 − 𝑏 2
2
+ 2
=1
𝑎 𝑏
a>b Horizontal 𝑎
e=c/a (0,±𝑐) y-Axis (0,±𝑎) NA 2a 2b 2𝑏2 𝑐 2 = 𝑎2 − 𝑏 2
<1 𝑦2 𝑥2
2
+ =1 𝑎
𝑎 𝑏2
Vertical
Hyperbola (±𝑐, 0) x-Axis (±𝑎, 0) NA 2a 2b 2𝑏2 𝑐 2 = 𝑎2 + 𝑏 2
𝑥2 𝑦2
e=c/a − =1 𝑎
𝑎2 𝑏2
>1 Horizontal
(0,±𝑐) y-Axis (0,±𝑎) NA 2a 2b 2𝑏2 𝑐 2 = 𝑎2 + 𝑏 2
𝑦2 𝑥2
2
− =1 𝑎
𝑎 𝑏2
Vertical

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