Q. 174.8( 5 Votes )
Find the equation of the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
Answer :
Given: the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
To find:
The equation of the required line.
Concept Used:
Point of intersection of two lines.
Explanation:
5x – 6y – 1 = 0 …… (i)
3x + 2y + 5 = 0 …… (ii)
By solving equation (i) and (ii) ,By cross multiplication,
⇒ x , y
Point of intersection ( - 1, - 1)
Now, the slope of the line 3x – 5y + 11 = 0 or yis
Now, we know that rhe product of the slope of two perpendicular lines is - 1.
Assuming: the slope of required line is m
⇒
Now, the equation of the required line passing through ( - 1, - 1) and having slope is given by,
Y + 1
⇒ 3y + 3 = - 5x – 5
⇒ 5x + 3y + 8 = 0
Hence, equation of required line is 5x + 3y + 8 = 0.
Rate this question :






















Find the equation of the line drawn through the point of intersection of the lines x + y = 9 and 2x – 3y + 7 = 0 and whose slope is .
Find the equation of the line drawn through the point of intersection of the lines x – y = 7 and 2x + y = 2 and passing through the origin.
RS Aggarwal - MathematicsFind the equation of the line drawn through the point of intersection of the lines x – 2y + 3 = 0 and 2x – 3y + 4 = 0 and passing through the point (4, -5).
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines 2x – 3y + 1 = 0 and x + y – 2 = 0 and drawn parallel to y-axis.
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines x – 7y + 5 = 0 and 3x + y – 7 = 0 and which is parallel to x-axis.
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and which is perpendicular to the line x + 2y + 1 = 0.
RS Aggarwal - MathematicsFind the equation of the line through the intersection of the lines 5x – 3y = 1 and 2x + 3y = 23 and which is perpendicular to the line 5x – 3y = 1.
RS Aggarwal - MathematicsFind the equation of the line drawn through the point of intersection of the lines x – y = 1 and 2x – 3y + 1 = 0 and which is parallel to the line 3x + 4y = 12.
RS Aggarwal - MathematicsFind the equation of the line passing through the intersection of the lines 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
RD Sharma - MathematicsProve that the lines ,
,
and
form a rhombus.