Q. 55.0( 3 Votes )

Find the equation

Answer :

Suppose the given two lines intersect at a point P(x1, y1). Then, (x1, y1) satisfies each of the given equations.

5x – 3y = 1 …(i)


2x + 3y = 23 …(ii)


Now, we find the point of intersection of eq. (i) and (ii)


Adding eq. (i) and (ii) we get


5x – 3y + 2x + 3y = 1 + 23


7x = 24



Putting the value of x in eq. (i), we get








Hence, the point of intersection P(x1, y1) is



Now, we know that, when two lines are perpendicular, then the product of their slope is equal to -1


m1 × m2 = -1


Slope of the given line × Slope of the perpendicular line = -1


Slope of the perpendicular line


The slope of the perpendicular line


So, the slope of a line which is perpendicular to the given line is


Then the equation of the line passing through the point having slope


y – y1 = m (x – x1)







63x + 105y – 781 = 0



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