JEE Main Coordinate Geometry: Complete Guide to Conics and Lines
Coordinate Geometry accounts for 5-6 JEE Main Maths questions. It is highly formulaic — if you master the standard forms and properties, most questions become mechanical. Here is your complete guide.
Straight Lines (1-2 questions)
Key formulas: Distance from point to line, angle between lines, area of triangle with vertices. JEE Main questions on lines often involve: angle bisectors, family of lines through intersection, and distances. Practice: finding equation of line satisfying multiple conditions.
Circles (2 questions)
Standard form, general form, finding center/radius from general equation. Key results: Power of a point, radical axis, coaxial circles. Tangent length from external point. Two-circle questions: common tangents, angle of intersection.
Parabola (1 question)
Standard parabola (y² = 4ax) properties: focus, directrix, latus rectum. Tangent and normal equations. Focal chord property. JEE often asks: find length of chord, locus of midpoint of chord, or tangent intersection locus.
Ellipse and Hyperbola (1 question each)
For Ellipse: standard form, eccentricity, directrices, focal radii sum = 2a. For Hyperbola: similar properties, asymptotes equation. Conjugate hyperbola. JEE Main often tests properties of tangent/normal to these curves.
Coordinate Geometry Speed Tips
Memorize: distance formula, section formula, centroid, circumcenter, orthocenter of triangle. These appear as 30-second questions. For conic sections, identify the type first, then apply standard formulas.
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