Advertisements
Advertisements
प्रश्न
Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers
Advertisements
उत्तर
The equations of the given straight lines are
y = 5x + b .......(1)
3x – 4y = 6 .......(2)
To find atleast two equations from the family y = 5x + b for which b is an integer and x-coordinate of the point of intersection of (1) and (2) is an integer.
Solving (1) and (2) using equation (1) inequation (2) (2)
⇒ 3x – 4(5x + b) = 6
3x – 20x – 4b = 6
– 17x = 6 + 4b
x = `(6 + 4"b")/(- 17)`
When b = 7
We have x = `(6 + 28)/(- 17)`
= `34/(- 17)`
= – 2
The corresponding equation of the line is = 5x + 7
When b = – 10
We have x = `(6 - 40)/(- 17)`
= `(- 34)/(- 17)`
= 2
The corresponding equation of the line is y = 5x – 10
Thus y = 5x + 7 and y = 5x – 10 are the two straight lines belonging to the family such that b is an integer and the x-coordinate of the point of intersection with the line (2) is an integer.
APPEARS IN
संबंधित प्रश्न
Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines
Find the equation of the straight line parallel to 5x − 4y + 3 = 0 and having x-intercept 3
Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15
If p1 and p2 are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ – y sin θ = a cos 2θ, then prove that p12 + p22 = a2
Find the distance between the parallel lines
12x + 5y = 7 and 12x + 5y + 7 = 0
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Find the family of straight lines parallel to 3x + 4y – 12
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A
A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq.units
Find the image of the point (−2, 3) about the line x + 2y − 9 = 0
Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers
Choose the correct alternative:
The slope of the line which makes an angle 45° with the line 3x − y = −5 are
Choose the correct alternative:
The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are
Choose the correct alternative:
The equation of the line with slope 2 and the length of the perpendicular from the origin equal to `sqrt(5)` is
Choose the correct alternative:
A line perpendicular to the line 5x − y = 0 forms a triangle with the coordinate axes. If the area of the triangle is 5 sq.units, then its equation is
Choose the correct alternative:
If a vertex of a square is at the origin and its one side lies along the line 4x + 3y − 20 = 0, then the area of the square is
Choose the correct alternative:
If the lines represented by the equation 6x2 + 41xy – 7y2 = 0 make angles α and β with x-axis then tan α tan β =
Choose the correct alternative:
θ is acute angle between the lines x2 – xy – 6y2 = 0 then `(2costheta + 3sintheta)/(4costheta + 5costheta)`
