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Conic Sections are a key chapter in JEE Maths, forming an essential part of coordinate geometry. They are curves obtained by cutting a cone with a plane and include parabola, ellipse, and hyperbola. Mastering conic sections helps students solve coordinate geometry problems related to tangents, normals, foci, directrix, and loci. At StudentBro.in, we provide a complete guide covering formulas, properties, examples, and practice problems to help JEE aspirants excel in this chapter.
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A conic section is the curve formed by the intersection of a plane with a double-napped cone. The three major types are:
Parabola – Plane parallel to a generator of the cone
Ellipse – Plane cuts only one nappe at an angle
Hyperbola – Plane cuts both nappes of the cone
Each curve has a focus, directrix, and eccentricity (e)
Eccentricity determines the type: Parabola (e=1), Ellipse (01)
A parabola is the set of all points equidistant from a focus and a directrix.
Standard forms:
Vertical axis: y² = 4ax
Horizontal axis: x² = 4ay
Focus: (a,0) for y² = 4ax
Directrix: x = -a
Example: y² = 8x → a = 2, Focus = (2,0), Directrix: x = -2
An ellipse is the set of points where the sum of distances from two foci is constant.
Standard form:
Horizontal: x²/a² + y²/b² = 1
Vertical: x²/b² + y²/a² = 1 (a > b)
Foci: (±√(a²-b²), 0) for horizontal ellipse
Major axis: 2a
Minor axis: 2b
Example: x²/9 + y²/4 = 1 → a² = 9, b² = 4, Foci = (±√5,0)
A hyperbola is the set of points where the difference of distances from two foci is constant.
Standard form:
Horizontal: x²/a² - y²/b² = 1
Vertical: y²/a² - x²/b² = 1
Foci: (±√(a² + b²), 0) for horizontal hyperbola
Vertices: (±a, 0)
Example: x²/9 - y²/4 = 1 → a² = 9, b² = 4, Foci = (±√13,0)
Parabola: y = mx + a/m (slope form)
Ellipse: y = ±(b/a)√(1-x²/a²) (point form)
Hyperbola: y = m x ± √(a²m² - b²) (slope form)
Tangent properties are widely used in JEE Main & Advanced coordinate geometry questions
Normal is perpendicular to the tangent at a point
Equation of normal to parabola y² = 4ax at (x₁,y₁): y - y₁ = -x₁/(2a)(x - x₁)
Normals are used for locus and orthogonal trajectory problems
Parabola: e = 1
Ellipse: e = √(1 - b²/a²)
Hyperbola: e = √(1 + b²/a²)
Understanding focus, directrix, and eccentricity helps in tangent, normal, and locus problems
Find points of intersection by solving equations of line and conic
Used for line cutting conics, chord problems, and area determination
Example: y = 2x intersects parabola y² = 4x → Solve (2x)² = 4x → x = 0,1 → Points (0,0),(1,2)
Solve tangent, normal, and intersection problems
Determine equation of parabola, ellipse, and hyperbola from given data
Solve chord length, slope, and foci problems
Useful for coordinate geometry, mechanics, optics, and loci problems
Regular practice ensures speed and accuracy in JEE Main & Advanced
Memorize standard forms of parabola, ellipse, hyperbola
Learn tangent, normal, focus-directrix, and eccentricity formulas
Solve problems using parametric coordinates for speed
Draw diagrams to visualize tangents, normals, and intersections
Practice previous year JEE conic sections problems for efficiency
At StudentBro.in, students can access:
Step-by-step explanations for parabola, ellipse, and hyperbola equations
Worked examples for tangent, normal, and intersection problems
Practice questions with solutions and shortcuts
Tips for quick problem-solving and exam strategy
Revision notes for last-minute preparation
Find the focus and directrix of y² = 8x
Find foci of ellipse x²/9 + y²/4 = 1
Find tangent to parabola y² = 4x at point (4,4)
Find intersection points of line y = 2x with parabola y² = 4x
Find eccentricity of hyperbola x²/16 - y²/9 = 1
Regular practice improves accuracy, speed, and confidence in solving conic sections problems in JEE exams.
Conic Sections are a vital chapter in JEE Maths. Understanding parabolas, ellipses, hyperbolas, tangents, normals, focus-directrix, and eccentricity allows students to solve coordinate geometry problems efficiently. At StudentBro.in, we provide a complete guide from basics to advanced problem-solving, making conic sections simple, practical, and exam-oriented.
Mastering this topic ensures students can tackle tangency, intersection, and foci problems confidently in both JEE Main and Advanced exams.
