🔮 Conic Sections Eccentricity Visualizer
Coordinate GeometryWhat's happening? e = 0: circle. 0 < e < 1: ellipse. e = 1: parabola. e > 1: hyperbola. The eccentricity controls the shape — one slider, four conics.
Conic sections: 4-6 questions every year.
JEE tests parabola, ellipse, hyperbola, tangents, normals.
Key formulas
Conic Sections Formulas
Parabola
y^2 = 4ax, focus (a,0)
Directrix x = -a
Ellipse
x^2/a^2 + y^2/b^2 = 1
c^2 = a^2-b^2, e = c/a < 1
Hyperbola
x^2/a^2 - y^2/b^2 = 1
c^2 = a^2+b^2, e > 1
Eccentricity
e=0:circle, <1:ellipse, =1:parabola, >1:hyperbola
Unifies conics
Step-by-step problem solving
How to solve maths problems in JEE
- Identify conic from equation
- Find a, b, c, e
- Use standard properties
- Tangents/normals: point-slope
Common JEE mistakes
What students get wrong
a vs b
a = semi-major (ellipse) or semi-transverse (hyperbola)
c formula
Ellipse: c^2=a^2-b^2. Hyperbola: c^2=a^2+b^2
Eccentricity direction
e<1 ellipse, e>1 hyperbola
Asymptote slope
y = +/-(b/a)x, not (a/b)
FAQs
Conic Sections Questions
Identify conic from equation?
Discriminant B^2-4AC of general form
Latus rectum?
Chord through focus. Parabola: 4a, Ellipse/Hyperbola: 2b^2/a
Foci of ellipse?
c^2 = a^2-b^2. On major axis, 2c apart
Asymptotes?
y = +/-(b/a)x for x^2/a^2 - y^2/b^2 = 1