### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Condition of coincidence of lines

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and coincidence lines if

But in parallel lines, the condition satisfy

Point of Intersection:

If two disticnt lines   and , represented by the equations

intersect at

then

Note:

then

(i) if   then   and   intersect at one point and it have unique solution.

(ii) If , then   and    never intesect, where   and   are parallel lines and having no solution.

(iii) If , then   and    are coincidenc linea and having infinitel many solutions.

Examples for Corresponding Conditions:

(i)

(ii)

(iii)

Family of lines through the point of intersection of two lines:

Let   -(i)

-(ii)

Now consider the equation   -(iii), represents family or system of lines where .

Conditions:

, represents family of lines.

(i) through the point of intersections   and , if they intersect.

(ii) parallel to   and , if they are parallel.

Examples for Corresponding Conditions:

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