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If the points \( (2,1), (2 ,7) \) and \( ( 5, x) \) are collinear , then find the value of \( x \).
Let and are three collinear points.
Slope of
Slope of
What is the inclination of a line whose slope is \( \dfrac{1}{\sqrt{3}} \)
Find the equation of a line passing through \( ( 3,4) \) and inclined at an angle of \(150^o \) with positive direction of \( x \)axis.
Here ,
So, equation of the line is
Find the equation of a line joining the points \( (3,4) \) and \( (2,5) \).
Given and
Equation of the line is
Angle between two lines is \(\dfrac{\pi}{4} \) and slope of one of them is \( \dfrac{1}{3} \) the slope of the other line.
Find the equation of the line which passes through the point \( (3,2) \) and making angle \( 60^o \) with the line \( \sqrt{3}x+y=1 \)
Given line is
Slope . Let slope of required line is .
Equation of the line is
Find the equation of the straight line that has \( y \)intercept \( 5 \) and is parallel to the straight line \( 3x7y=8 \)
Given .
Slope .
Slope of the required line is also intercept of the required line
Two sides of a square lie on the lines \( 5x12y+6=0 \) and \( 5x12y=20 \) what is its area?
The length of the side of the square is equal to the distance to the parallel lines.
Now, distance between the parallel lines
Find the area of the parallelogram whose sides are \( x+2y+3=0 ,\quad 3x+4y5=0,\quad 2x+4y+5=0 \) and \( 3x+4y10=0 \)
Here
Find the equation of the line that passes through the point \( (3, 4) \) and perpendicular to the line\(3x+2y+5=0 \)
Slope of the given line
Slope of the required line
(Since the required line is perpendicular to the given line.)
It passes through . So, equation of the line is
Find the distance between the line \(3x4y+8=0 \) and the point \((2, 3) \)
Given line and point
Find the foot of perpendicular of the line drawn from\( P ( 2, 3) \) on the line \( x2y+5=0\)
Hence,
Find the image of the point \( P ( 1 ,2) \)in the mirror \(2x3y+4=0 \)
The image of about the line is
Find the equation of bisector of the angle between the lines \( 3x+y+1=0 \) and \( x+3y+1=0 \)
Equation of bisectors are
Taking positive sign
Taking negative sign
If \( 3a+2b+5c=0 \) and the set of lines \(ax+by+c=0 \) passes through a fixed point. Find coordinates of that point.
lies on the line
Hence fixed point is
Obtain the equations of the line through the intersection of lines \( 3x+7y=17 \) and \( x+2y=5 \) and perpendicular to the straight line \( 3x+4y=10 \)
The equation of any line passing through the intersection of lines is
(i)
This is perpendicular to
Putting the value of in (i), the equation of the required line
Find the angle between the pair of straight lines \( x^23xy+2y^2=0 \)
Given,
Hence
Now
or
Find the equation of the bisectores of the angle between the line represented by \(3x^25xy+4y^2=0 \)
(Given)
Hence
Equation of bisectors of the angle between pair of lines is
Find the equations to the pair of lines through origin which are perpendicular to the lines represented by \( 6x^2xy12y^2=0 \)
We have
The equations of the lines passing through origin and perpendicular to the given lines are and .
Their combined equation is
Find the equation of the straight line which passes through the point \( (1, 2) \) and cuts off equal intercept from axes.
Equation of line
Since lies on the line,
(i)
Putting the value of in (i)