Coordinate Geometry
Board: JEE Advanced |Exam:JEEAdvanced
JEEAdvancedstudynotesforCoordinateGeometrybyAjayYadav.In-depthcoverageofadvancedtopicsandproblem-solvingtechniques.
KeyConcepts
AdvancedConics
Pairofstraightlines:ax²+2hxy+by²+2gx+2fy+c=0.Conditionforlines:Δ=0.Anglebetweenlines:tanθ=|2√h²-ab|/(a+b).
Circle and System of Circles
Radical axis. Coaxial system. Limiting points. Angle between circles. Orthogonal circles condition: 2gg’+2ff’=c+c’.
Detailed Conics
Parabola: focal chord properties, chord of contact. Ellipse: auxiliary circle, director circle, chord of contact. Hyperbola: conjugate hyperbola, rectangular hyperbola properties.
Important Formulas
| Pair of lines angle | tanθ = 2√h²-ab/(a+b) |
| Orthogonal circles | 2gg'+2ff'=c+c' |
| Director circle (ellipse) | x²+y²=a²+b² |
Solved Examples
Example 1: Find angle between lines represented by x²+2xy+y²=0.
Solution: a=b=1, h=1. h²-ab=0. Lines are coincident.
Practice Questions
- Find condition for ax²+2hxy+by²=0 to represent perpendicular lines.
- Check orthogonality: x²+y²-2x+4y-4=0 and x²+y²+4x-6y+9=0.
- Find director circle of ellipse x²/16+y²/9=1.
- Find the radical axis of x²+y²=9 and (x-3)²+y²=9.
- If lines represented by x²-2xy-3y²=0, find angle between them.