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Point of Intersection Formula - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Point of intersection of two lines is considered one of the most asked concept.

  • 40 Questions around this concept.

Solve by difficulty

QuestionEASY

 Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0   and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then :

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The equation of a straight line passing through the point of intersection of \mathrm{x-y+1=0} and \mathrm{3 x+y-5=0} and perpendicular to one of them is:

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The values of \mathrm{k} for which lines \mathrm{\mathrm{kx}+2 \mathrm{y}+2=0,2 \mathrm{x}+\mathrm{ky}+3=0,3 \mathrm{x}+3 \mathrm{y}+\mathrm{k}=0} are concurrent:

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The number of integer values of \mathrm{m}, for which the \mathrm{x}-coordinate of the point of intersection of the lines \mathrm{3 x+4 y=9} and \mathrm{y=m x+1} is also an integer, is:

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Concepts Covered - 1

Point of intersection of two lines

Point of intersection of two lines

If the equations of two non-parallel lines are 

\\L_1=a_1x+b_1y+c_1=0\\L_2=a_2x+b_2y+c_2=0

If P (x1, y1) is a point of intersection of L1 and L2 , then solving these two equations of the line by cross multiplication

\frac{x_1}{b_1c_2-c_1b_2}=\frac{y_1}{c_1a_2-a_1c_2}=\frac{1}{a_1b_2-b_1a_2}

We get,

\mathbf{\left ( x_1,y_1 \right )=\left ( \frac{b_1c_2-b_2c_1}{a_1b_2-a_2b_1},\frac{c_1a_2-c_2a_1}{a_1b_2-a_2b_1} \right )}

 

Concurrent Lines

If three straight lines meet in a point then three given lines are called concurrent.

To check if three lines are concurrent or not

  1. First find the point of intersection of any two straight lines by solving them simultaneously. If this point satisfies the third equation then three lines are concurrent.

  2. Three lines  a_{i} x+b_{i} y+c_{i}=0 , i = 1, 2, 3 are concurrent if \left|\begin{array}{lll} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}\right|=0.

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Point of intersection of two lines

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