Conic Section Calculator
This tool determines the nature and the characteristics of a conic section from its equation. It includes Parabola, Ellipse, hyperbola and Circle.
Answer
Conic section type : Ellipse
Center : `( -5/8 , 7/2 )`
Semimajor axis : `1/4*sqrt(109)`
Semiminor axis : `1/8*sqrt(109)`
Standard equation : `(x - x_c)^2/a^2 + (y - y_c)^2/b^2 = 1`
`(x_c , y_c) = ( -5/8 , 7/2 )`
`(a^2 , b^2) = ( 109/64 , 109/16 )`
Focal axis : line of equation `x = -5/8`
Non focal axis : line of equation `y = 7/2`
Focal distance : `1/4*sqrt(327)`
Foci : `( -5/8 , -1/8*sqrt(327) + 7/2 )` and `( -5/8 , 1/8*sqrt(327) + 7/2 )`
Vertices : S1 `( -5/8 , -1/4*sqrt(109) + 7/2 )` , S2 `( -5/8 , 1/4*sqrt(109) + 7/2 )` , S3 `( 1/8*sqrt(109) - 5/8 , 7/2 )` , S4 `( -1/8*sqrt(109) - 5/8 , 7/2 )`
Eccentricity : `e = 1/218*sqrt(327)*sqrt(109)`
See this conic graphDo you have any suggestions to improve this page ?
Center : `( -5/8 , 7/2 )`
Semimajor axis : `1/4*sqrt(109)`
Semiminor axis : `1/8*sqrt(109)`
Standard equation : `(x - x_c)^2/a^2 + (y - y_c)^2/b^2 = 1`
`(x_c , y_c) = ( -5/8 , 7/2 )`
`(a^2 , b^2) = ( 109/64 , 109/16 )`
Focal axis : line of equation `x = -5/8`
Non focal axis : line of equation `y = 7/2`
Focal distance : `1/4*sqrt(327)`
Foci : `( -5/8 , -1/8*sqrt(327) + 7/2 )` and `( -5/8 , 1/8*sqrt(327) + 7/2 )`
Vertices : S1 `( -5/8 , -1/4*sqrt(109) + 7/2 )` , S2 `( -5/8 , 1/4*sqrt(109) + 7/2 )` , S3 `( 1/8*sqrt(109) - 5/8 , 7/2 )` , S4 `( -1/8*sqrt(109) - 5/8 , 7/2 )`
Eccentricity : `e = 1/218*sqrt(327)*sqrt(109)`
See this conic graphDo you have any suggestions to improve this page ?
How to use this calculator ?
To calculate the type and characteristics of a conic section, select its equation type and input the coefficients. You can input,
- Numbers
- Fractions
- Operators : + - * / ^ (power)
To input a square root, use 'power 1/2'. For example, square root of 5 = 5^(1/2)
- Constants : pi and e
Example
Let's calculate the nature and details of the conic section of equation,
`4x^2+y^2+5x-7y+7=0`
In the calculator, select the following Equation type : `A*x^2+B*y^2+C*x+D*y+E=0`
and input A = 4, B = 1 , C = 5 , D = -7 and E = 7
The result is the following calculator.
See also
Ellipse calculator
Parabola calculator
Hyperbola calculator
Circle calculator
Conic sections calculators
Geometry calculators
Mathematics calculators