JEE PREP | APRIL 2026
JEE MAIN 2027 — CHAPTER-WISE PRACTICE & STRATEGY | MATHEMATICS
• Subject: Mathematics — Coordinate Geometry
• Expected questions: 5–7 per year in JEE Main
• Difficulty: Moderate (straight lines, circles) to High (conics)
• Contributes ~17–20% of Mathematics marks in JEE Main
Coordinate Geometry is one of the highest-weightage topics in JEE Main Mathematics, consistently contributing 5–7 questions every year. The chapter spans straight lines, circles, parabolas, ellipses, and hyperbolas — all rooted in the Cartesian coordinate system. A strong command over standard forms, parametric equations, and key properties of each conic section is indispensable for JEE 2027 aspirants.
Get expert guidance with our JEE coaching program. Test your preparation with our free JEE mock test. View complete chapter-wise breakdown in the JEE Main syllabus.
1. Straight Lines and Circles — Foundations
• Slope of line through (x₁,y₁) and (x₂,y₂): m = (y₂−y₁)/(x₂−x₁)
• Collinear points: Area of triangle = 0
• Angle between two lines: tan θ = |m₁−m₂|/|1+m₁m₂|
• Distance from point (x₁,y₁) to line ax+by+c=0: d = |ax₁+by₁+c|/√(a²+b²)
• Concurrent lines: Determinant of coefficients = 0
• Slope-intercept: y = mx + c
• Point-slope: y − y₁ = m(x − x₁)
• Two-point form: (y−y₁)/(y₂−y₁) = (x−x₁)/(x₂−x₁)
• Intercept form: x/a + y/b = 1
• Normal form: x cosα + y sinα = p
• General form: ax + by + c = 0 (slope = −a/b)
Essential Formulas — Circles
• Standard form: (x−h)² + (y−k)² = r² (centre (h,k), radius r)
• General form: x² + y² + 2gx + 2fy + c = 0 (centre (−g,−f), radius = √(g²+f²−c))
• Tangent at (x₁,y₁): xx₁ + yy₁ + g(x+x₁) + f(y+y₁) + c = 0
• Length of tangent from external point: L = √(x₁²+y₁²+2gx₁+2fy₁+c)
2. Parabola, Ellipse, and Hyperbola — Conic Sections
Circle: e = 0 | Ellipse: 0 < e < 1 | Parabola: e = 1 | Hyperbola: e > 1
Parabola y² = 4ax: Vertex (0,0) | Focus (a,0) | Directrix x = −a | Axis: x-axis | Latus rectum = 4a
Parabola x² = 4ay: Vertex (0,0) | Focus (0,a) | Directrix y = −a | Axis: y-axis
• Centre: (0,0) | Foci: (±c, 0) where c² = a² − b²
• Eccentricity: e = c/a (0 < e < 1)
• Directrices: x = ±a/e | Latus rectum length = 2b²/a
• Sum of focal radii from any point = 2a
Essential Formulas — Hyperbola x²/a² − y²/b² = 1
• Foci: (±c, 0) where c² = a² + b²
• Eccentricity: e = c/a (e > 1)
• Asymptotes: y = ±(b/a)x
• Difference of focal radii from any point = 2a
| Topic | JEE Main 2022 | JEE Main 2023 | JEE Main 2024 | Expected 2027 |
|---|---|---|---|---|
| Straight Lines | 1–2 Q | 1–2 Q | 1–2 Q | 1–2 Q |
| Circles | 1–2 Q | 1–2 Q | 1–2 Q | 1–2 Q |
| Parabola | 1 Q | 1–2 Q | 1 Q | 1–2 Q |
| Ellipse | 1 Q | 1 Q | 1 Q | 1 Q |
| Hyperbola | 0–1 Q | 1 Q | 1 Q | 1 Q |
• Centroid of triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃): G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
• Locus problems: Eliminate the parameter to get the equation
• For tangent from external point to parabola y² = 4ax: y = mx + a/m
• Common tangent to circle and parabola — high-frequency JEE topic
• Reflection of point (h,k) in line ax+by+c=0: use formula directly
3. JEE Main 2027 — 10 MCQ Practice Questions
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4. Frequently Asked Questions (FAQ)
Q1: How many questions come from Coordinate Geometry in JEE Main?
Coordinate Geometry contributes approximately 5–7 questions in JEE Main, making it one of the top 3 topics in Mathematics alongside Calculus and Algebra. Circles and parabolas appear almost every year, while ellipse and hyperbola alternate in frequency.
Q2: What is the most important formula to remember for JEE circles?
The general equation x² + y² + 2gx + 2fy + c = 0 and its conversion to standard form is critical. The condition for two circles to be orthogonal (2g₁g₂ + 2f₁f₂ = c₁ + c₂) is frequently tested. The length of the common chord and radical axis problems are also high-frequency.
Q3: What is the parametric form of a parabola y² = 4ax?
The parametric coordinates are (at², 2at) where t is the parameter. This form simplifies tangent equations to ty = x + at² and helps in finding chords of contact, normals, and locus problems efficiently.
Q4: What topics in Coordinate Geometry are easiest to score in JEE Main?
Straight lines (distance formulas, section formula, area of triangle) and basic circle questions (finding centre, radius, tangent length) are the most straightforward. Always secure these before attempting harder conic section problems.
Q5: How do you find the common tangent between a circle and a parabola?
Write the tangent to the parabola in slope form y = mx + a/m, then apply the condition that its perpendicular distance from the circle’s centre equals the radius. Solve for m to get the slope(s) of common tangents.
Last Updated: April 2026