Coordinate geometry Straight line Topics - IIT JEE Syllabus

1

Various forms of equations of a line

2m2/10

📌 Key FormulaSlope-intercept: y = mx + c, Point-slope: y - y₁ = m(x - x₁), Two-point: (y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁), Intercept: x/a + y/b = 1

2

Intersection of lines

2m2/10

📌 Key FormulaSolving linear equations simultaneously to get point of intersection.

3

Angles between two lines

2m2/10

📌 Key Formulatan θ = |(m₂ - m₁)/(1 + m₁ m₂)|

4

Conditions for concurrence of three lines

2m3/10

📌 Key FormulaThree lines are concurrent if point of intersection of any two lies on the third, or determinant of coefficients is zero.

5

The distance of a point form a line

2m2/10

📌 Key FormulaDistance of (x₁, y₁) from line Ax + By + C = 0 is |Ax₁ + By₁ + C| / √(A² + B²)

6

Equations of internal and external by sectors of angles between two lines coordinate of the centroid

2m4/10

📌 Key FormulaInternal bisector: (A₁x + B₁y + C₁)/√(A₁²+B₁²) = ± (A₂x + B₂y + C₂)/√(A₂²+B₂²). Centroid of triangle: ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

7

circumcentre of a triangle

2m4/10

📌 Key FormulaPoint equidistant from vertices, intersection of perpendicular bisectors.

8

Equation of the family of lines passing through the point of intersection of two lines

2m3/10

📌 Key FormulaL₁ + λL₂ = 0, where L₁=0 and L₂=0 are given lines.

9

Orthocentre of a triangle

2m2/10

📌 Key FormulaIntersection of altitudes.

10

Incentre of a triangle

2m2/10

📌 Key FormulaIntersection of angle bisectors.